Chapter 56: Area of 2D Shapes
Learn Grade 3 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Area of 2D Shapes with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Area as covering space (a Grade 3 idea used in this chapter)
- Square units (a Grade 3 idea used in this chapter)
- Counting square units (a Grade 3 idea used in this chapter)
- Area of rectangles by counting rows (a Grade 3 idea used in this chapter)
- Area of simple irregular shapes on grids (a Grade 3 idea used in this chapter)
- Comparing areas (a Grade 3 idea used in this chapter)
- Drawing a shape with a given area (a Grade 3 idea used in this chapter)
- Different shapes with the same area (a Grade 3 idea used in this chapter)
- Estimating area (a Grade 3 idea used in this chapter)
- Area word problems (a Grade 3 idea used in this chapter)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
56.1 Area as covering space
Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Area as covering space?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Area as covering space?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Area as covering space.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Area as covering space problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Area as covering space.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area as covering space can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Area as covering space. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.2 Square units
Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Square units?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Square units?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Square units.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Square units problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Square units.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Square units can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Square units in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Square units and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Square units using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Square units problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Square units could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Square units. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.3 Counting square units
Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Counting square units?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Counting square units?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Counting square units.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Counting square units problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Counting square units.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Counting square units can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Counting square units in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Counting square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Counting square units and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Counting square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Counting square units using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Counting square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Counting square units problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Counting square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Counting square units could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Counting square units becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Counting square units. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.4 Area of rectangles by counting rows
Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Area of rectangles by counting rows?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Area of rectangles by counting rows?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Area of rectangles by counting rows.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Area of rectangles by counting rows problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Area of rectangles by counting rows.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area of rectangles by counting rows can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180 - 35 = 145.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 145°
Worked Example 7
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180 - 48 = 132.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 132°
Worked Example 8
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180 - 67 = 113.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 113°
Worked Example 9
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180 - 72 = 108.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 108°
Worked Example 10
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180 - 110 = 70.
Very beginner explanation: Angles on a straight line total 180°.
Answer: 70°
Practice Exercise
Create one new question about Area of rectangles by counting rows. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.5 Area of simple irregular shapes on grids
Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Area of simple irregular shapes on grids?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Area of simple irregular shapes on grids?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Area of simple irregular shapes on grids.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Area of simple irregular shapes on grids problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Area of simple irregular shapes on grids.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area of simple irregular shapes on grids can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Area of simple irregular shapes on grids. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.6 Comparing areas
Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Comparing areas?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Comparing areas?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Comparing areas.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Comparing areas problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Comparing areas.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Comparing areas can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Comparing areas. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.7 Drawing a shape with a given area
Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Drawing a shape with a given area?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Drawing a shape with a given area?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Drawing a shape with a given area.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Drawing a shape with a given area problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Drawing a shape with a given area.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Drawing a shape with a given area can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Drawing a shape with a given area. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.8 Different shapes with the same area
Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Different shapes with the same area?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Different shapes with the same area?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Different shapes with the same area.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Different shapes with the same area problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Different shapes with the same area.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Different shapes with the same area can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Different shapes with the same area. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.9 Estimating area
Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Estimating area?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Estimating area?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Estimating area.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Estimating area problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Estimating area.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Estimating area can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Estimating area. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
56.10 Area word problems
Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Area word problems?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Worked Example 2
Problem: What should you identify first before solving a problem about Area word problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Area word problems.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Area word problems problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Area word problems.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Answer: Area word problems can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the area of a rectangle 6 cm by 3 cm.
- Use A = length × width.
- A = 6 × 3.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 18 cm²
Worked Example 7
Problem: Find the area of a rectangle 7 cm by 4 cm.
- Use A = length × width.
- A = 7 × 4.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 28 cm²
Worked Example 8
Problem: Find the area of a rectangle 8 cm by 5 cm.
- Use A = length × width.
- A = 8 × 5.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 40 cm²
Worked Example 9
Problem: Find the area of a rectangle 9 cm by 6 cm.
- Use A = length × width.
- A = 9 × 6.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 54 cm²
Worked Example 10
Problem: Find the area of a rectangle 10 cm by 7 cm.
- Use A = length × width.
- A = 10 × 7.
Very beginner explanation: Area measures the 2D space inside a figure and uses square units.
Answer: 70 cm²
Practice Exercise
Create one new question about Area word problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Area as covering space.
- Create and solve one original problem about Square units.
- Create and solve one original problem about Counting square units.
- Create and solve one original problem about Area of rectangles by counting rows.
- Create and solve one original problem about Area of simple irregular shapes on grids.
- Create and solve one original problem about Comparing areas.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Area as covering space?
Answer: Area as covering space develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q2. What is the key idea in Square units?
Answer: Square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q3. What is the key idea in Counting square units?
Answer: Counting square units is an important Grade 3 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q4. What is the key idea in Area of rectangles by counting rows?
Answer: Area of rectangles by counting rows develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q5. What is the key idea in Area of simple irregular shapes on grids?
Answer: Area of simple irregular shapes on grids develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q6. What is the key idea in Comparing areas?
Answer: Comparing areas develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q7. What is the key idea in Drawing a shape with a given area?
Answer: Drawing a shape with a given area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q8. What is the key idea in Different shapes with the same area?
Answer: Different shapes with the same area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q9. What is the key idea in Estimating area?
Answer: Estimating area develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q10. What is the key idea in Area word problems?
Answer: Area word problems develops spatial reasoning through shapes, position, movement, measurement, and labelled diagrams.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 3 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Area of 2D Shapes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Area of 2D Shapes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Area of 2D Shapes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Area of 2D Shapes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Area of 2D Shapes effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.