Chapter 53: Perimeter, Area, and Surface Area

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review

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Chapter Overview

This chapter teaches Perimeter, Area, and Surface Area in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

Perimeter (Perimeter is the total distance around a two-dimensional shape.)
Area (Area measures the amount of two-dimensional space inside a shape.)
Composite area (A composite number has more than two positive factors.)
Finding missing dimensions (Finding missing dimensions is a Grade 6 mathematics idea in Perimeter, Area, and Surface Area. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Surface area (Surface area is the total area of all outside faces of a three-dimensional object.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

53.1 Perimeter

Perimeter is the total distance around a two-dimensional shape. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the perimeter of a rectangle 5 cm by 2 cm.

Use P = 2(l + w).
P = 2(5+2).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 14 cm

Worked Example 2

Problem: Find the perimeter of a rectangle 6 cm by 3 cm.

Use P = 2(l + w).
P = 2(6+3).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 18 cm

Worked Example 3

Problem: Find the perimeter of a rectangle 7 cm by 4 cm.

Use P = 2(l + w).
P = 2(7+4).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 22 cm

Worked Example 4

Problem: Find the perimeter of a rectangle 8 cm by 5 cm.

Use P = 2(l + w).
P = 2(8+5).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 26 cm

Worked Example 5

Problem: Find the perimeter of a rectangle 9 cm by 6 cm.

Use P = 2(l + w).
P = 2(9+6).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 30 cm

Worked Example 6

Problem: Find the perimeter of a rectangle 10 cm by 7 cm.

Use P = 2(l + w).
P = 2(10+7).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 34 cm

Worked Example 7

Problem: Find the perimeter of a rectangle 11 cm by 8 cm.

Use P = 2(l + w).
P = 2(11+8).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 38 cm

Worked Example 8

Problem: Find the perimeter of a rectangle 12 cm by 9 cm.

Use P = 2(l + w).
P = 2(12+9).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 42 cm

Worked Example 9

Problem: Find the perimeter of a rectangle 13 cm by 10 cm.

Use P = 2(l + w).
P = 2(13+10).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 46 cm

Worked Example 10

Problem: Find the perimeter of a rectangle 14 cm by 11 cm.

Use P = 2(l + w).
P = 2(14+11).

Very beginner explanation: Perimeter is a length around a boundary, so it uses linear units.

Answer: 50 cm

Practice Exercise

Create one new Grade 6 problem about Perimeter. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.2 Area

Area measures the amount of two-dimensional space inside a shape. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the area of a rectangle 5 cm by 2 cm.

Use A = length × width.
A = 5 × 2.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 10 cm²

Worked Example 2

Problem: Find the area of a rectangle 6 cm by 3 cm.

Use A = length × width.
A = 6 × 3.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 18 cm²

Worked Example 3

Problem: Find the area of a rectangle 7 cm by 4 cm.

Use A = length × width.
A = 7 × 4.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 28 cm²

Worked Example 4

Problem: Find the area of a rectangle 8 cm by 5 cm.

Use A = length × width.
A = 8 × 5.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 40 cm²

Worked Example 5

Problem: Find the area of a rectangle 9 cm by 6 cm.

Use A = length × width.
A = 9 × 6.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 54 cm²

Worked Example 6

Problem: Find the area of a rectangle 10 cm by 7 cm.

Use A = length × width.
A = 10 × 7.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 70 cm²

Worked Example 7

Problem: Find the area of a rectangle 11 cm by 8 cm.

Use A = length × width.
A = 11 × 8.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 88 cm²

Worked Example 8

Problem: Find the area of a rectangle 12 cm by 9 cm.

Use A = length × width.
A = 12 × 9.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 108 cm²

Worked Example 9

Problem: Find the area of a rectangle 13 cm by 10 cm.

Use A = length × width.
A = 13 × 10.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 130 cm²

Worked Example 10

Problem: Find the area of a rectangle 14 cm by 11 cm.

Use A = length × width.
A = 14 × 11.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 154 cm²

Practice Exercise

Create one new Grade 6 problem about Area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.3 Rectangle area

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Rectangle area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.4 Parallelogram area

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Parallelogram area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.5 Triangle area introduction

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Triangle area introduction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.6 Area of four-sided shapes

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: How many sides does a quadrilateral have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 2

Problem: How many pairs of parallel sides does a rectangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 2 pairs

Worked Example 3

Problem: How many right angles does a square have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 4

Worked Example 4

Problem: Does a rhombus have four equal side lengths?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 5

Problem: Can a trapezoid have a pair of parallel sides?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 6

Problem: Are opposite sides of a parallelogram parallel?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 7

Problem: How many sides does a triangle have?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 3

Worked Example 8

Problem: What angle do perpendicular lines form?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: 90°

Worked Example 9

Problem: Does a square also satisfy the properties of a rectangle?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Worked Example 10

Problem: Can line symmetry divide a figure into mirror-image halves?

Recall the defining properties of the shape or lines.
Match the question to those properties.

Very beginner explanation: Shape names are based on properties such as side lengths, parallel sides, and angles.

Answer: Yes

Practice Exercise

Create one new Grade 6 problem about Area of four-sided shapes. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.7 Composite area introduction

A composite number has more than two positive factors. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Is 37 prime or composite?

List or test its positive factors.
Factors: 1, 37.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Worked Example 2

Problem: Is 60 prime or composite?

List or test its positive factors.
Factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20....

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Composite

Worked Example 3

Problem: Is 79 prime or composite?

List or test its positive factors.
Factors: 1, 79.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Worked Example 4

Problem: Is 37 prime or composite?

List or test its positive factors.
Factors: 1, 37.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Worked Example 5

Problem: Is 80 prime or composite?

List or test its positive factors.
Factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Composite

Worked Example 6

Problem: Is 70 prime or composite?

List or test its positive factors.
Factors: 1, 2, 5, 7, 10, 14, 35, 70.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Composite

Worked Example 7

Problem: Is 31 prime or composite?

List or test its positive factors.
Factors: 1, 31.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Worked Example 8

Problem: Is 23 prime or composite?

List or test its positive factors.
Factors: 1, 23.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Worked Example 9

Problem: Is 81 prime or composite?

List or test its positive factors.
Factors: 1, 3, 9, 27, 81.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Composite

Worked Example 10

Problem: Is 47 prime or composite?

List or test its positive factors.
Factors: 1, 47.

Very beginner explanation: A prime has exactly two positive factors; a composite has more than two.

Answer: Prime

Practice Exercise

Create one new Grade 6 problem about Composite area introduction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.8 Finding missing dimensions

Finding missing dimensions is a Grade 6 mathematics idea in Perimeter, Area, and Surface Area. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the area of a rectangle 5 cm by 2 cm.

Use A = length × width.
A = 5 × 2.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 10 cm²

Worked Example 2

Problem: Find the area of a rectangle 6 cm by 3 cm.

Use A = length × width.
A = 6 × 3.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 18 cm²

Worked Example 3

Problem: Find the area of a rectangle 7 cm by 4 cm.

Use A = length × width.
A = 7 × 4.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 28 cm²

Worked Example 4

Problem: Find the area of a rectangle 8 cm by 5 cm.

Use A = length × width.
A = 8 × 5.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 40 cm²

Worked Example 5

Problem: Find the area of a rectangle 9 cm by 6 cm.

Use A = length × width.
A = 9 × 6.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 54 cm²

Worked Example 6

Problem: Find the area of a rectangle 10 cm by 7 cm.

Use A = length × width.
A = 10 × 7.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 70 cm²

Worked Example 7

Problem: Find the area of a rectangle 11 cm by 8 cm.

Use A = length × width.
A = 11 × 8.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 88 cm²

Worked Example 8

Problem: Find the area of a rectangle 12 cm by 9 cm.

Use A = length × width.
A = 12 × 9.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 108 cm²

Worked Example 9

Problem: Find the area of a rectangle 13 cm by 10 cm.

Use A = length × width.
A = 13 × 10.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 130 cm²

Worked Example 10

Problem: Find the area of a rectangle 14 cm by 11 cm.

Use A = length × width.
A = 14 × 11.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 154 cm²

Practice Exercise

Create one new Grade 6 problem about Finding missing dimensions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

53.9 Surface area

Surface area is the total area of all outside faces of a three-dimensional object. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the surface area of a rectangular prism 5 cm × 2 cm × 3 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(10+15+6).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 62 cm²

Worked Example 2

Problem: Find the surface area of a rectangular prism 6 cm × 3 cm × 4 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(18+24+12).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 108 cm²

Worked Example 3

Problem: Find the surface area of a rectangular prism 7 cm × 4 cm × 5 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(28+35+20).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 166 cm²

Worked Example 4

Problem: Find the surface area of a rectangular prism 8 cm × 5 cm × 6 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(40+48+30).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 236 cm²

Worked Example 5

Problem: Find the surface area of a rectangular prism 9 cm × 6 cm × 7 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(54+63+42).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 318 cm²

Worked Example 6

Problem: Find the surface area of a rectangular prism 10 cm × 7 cm × 8 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(70+80+56).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 412 cm²

Worked Example 7

Problem: Find the surface area of a rectangular prism 11 cm × 8 cm × 9 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(88+99+72).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 518 cm²

Worked Example 8

Problem: Find the surface area of a rectangular prism 12 cm × 9 cm × 10 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(108+120+90).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 636 cm²

Worked Example 9

Problem: Find the surface area of a rectangular prism 13 cm × 10 cm × 11 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(130+143+110).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 766 cm²

Worked Example 10

Problem: Find the surface area of a rectangular prism 14 cm × 11 cm × 12 cm.

Find the area of each pair of matching faces.
Add all six face areas.
SA = 2(154+168+132).

Very beginner explanation: Surface area measures the total outside covering of a 3D object.

Answer: 908 cm²

Practice Exercise

Create one new Grade 6 problem about Surface area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.10 Nets and surface area

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Describe a cube.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 faces, 12 edges, 8 vertices

Worked Example 2

Problem: Describe a rectangular prism.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 faces, 12 edges, 8 vertices

Worked Example 3

Problem: Describe a triangular prism.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 5 faces, 9 edges, 6 vertices

Worked Example 4

Problem: Describe a square pyramid.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 5 faces, 8 edges, 5 vertices

Worked Example 5

Problem: Describe a cylinder.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 2 circular bases and 1 curved surface

Worked Example 6

Problem: Describe a cube net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 connected squares

Worked Example 7

Problem: Describe a rectangular prism net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 rectangles, with some faces possibly squares

Worked Example 8

Problem: Describe a triangular prism net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 2 triangles and 3 rectangles

Worked Example 9

Problem: Describe a square pyramid net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 1 square and 4 triangles

Worked Example 10

Problem: Describe a 3D structure.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: can be described using faces, edges, vertices, and views

Practice Exercise

Create one new Grade 6 problem about Nets and surface area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.11 Rectangular-prism surface area

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Describe a cube.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 faces, 12 edges, 8 vertices

Worked Example 2

Problem: Describe a rectangular prism.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 faces, 12 edges, 8 vertices

Worked Example 3

Problem: Describe a triangular prism.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 5 faces, 9 edges, 6 vertices

Worked Example 4

Problem: Describe a square pyramid.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 5 faces, 8 edges, 5 vertices

Worked Example 5

Problem: Describe a cylinder.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 2 circular bases and 1 curved surface

Worked Example 6

Problem: Describe a cube net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 connected squares

Worked Example 7

Problem: Describe a rectangular prism net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 6 rectangles, with some faces possibly squares

Worked Example 8

Problem: Describe a triangular prism net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 2 triangles and 3 rectangles

Worked Example 9

Problem: Describe a square pyramid net.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: 1 square and 4 triangles

Worked Example 10

Problem: Describe a 3D structure.

Identify its flat faces or bases.
Count edges and vertices when those features apply.

Very beginner explanation: Three-dimensional objects can be compared by their faces, edges, vertices, bases, and nets.

Answer: can be described using faces, edges, vertices, and views

Practice Exercise

Create one new Grade 6 problem about Rectangular-prism surface area. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

53.12 Real-life area and surface-area problems

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Find the area of a rectangle 5 cm by 2 cm.

Use A = length × width.
A = 5 × 2.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 10 cm²

Worked Example 2

Problem: Find the area of a rectangle 6 cm by 3 cm.

Use A = length × width.
A = 6 × 3.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 18 cm²

Worked Example 3

Problem: Find the area of a rectangle 7 cm by 4 cm.

Use A = length × width.
A = 7 × 4.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 28 cm²

Worked Example 4

Problem: Find the area of a rectangle 8 cm by 5 cm.

Use A = length × width.
A = 8 × 5.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 40 cm²

Worked Example 5

Problem: Find the area of a rectangle 9 cm by 6 cm.

Use A = length × width.
A = 9 × 6.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 54 cm²

Worked Example 6

Problem: Find the area of a rectangle 10 cm by 7 cm.

Use A = length × width.
A = 10 × 7.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 70 cm²

Worked Example 7

Problem: Find the area of a rectangle 11 cm by 8 cm.

Use A = length × width.
A = 11 × 8.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 88 cm²

Worked Example 8

Problem: Find the area of a rectangle 12 cm by 9 cm.

Use A = length × width.
A = 12 × 9.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 108 cm²

Worked Example 9

Problem: Find the area of a rectangle 13 cm by 10 cm.

Use A = length × width.
A = 13 × 10.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 130 cm²

Worked Example 10

Problem: Find the area of a rectangle 14 cm by 11 cm.

Use A = length × width.
A = 14 × 11.

Very beginner explanation: Area covers a two-dimensional region, so it uses square units.

Answer: 154 cm²

Practice Exercise

Create one new Grade 6 problem about Real-life area and surface-area problems. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

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30 Review Questions and Answers

Q1. What is important to understand about Perimeter?

Answer: Perimeter is the total distance around a two-dimensional shape.

Q2. What is important to understand about Area?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q3. What is important to understand about Rectangle area?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q4. What is important to understand about Parallelogram area?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q5. What is important to understand about Triangle area introduction?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q6. What is important to understand about Area of four-sided shapes?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q7. What is important to understand about Composite area introduction?

Answer: A composite number has more than two positive factors.

Q8. What is important to understand about Finding missing dimensions?

Answer: Finding missing dimensions is a Grade 6 mathematics idea in Perimeter, Area, and Surface Area. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Surface area?

Answer: Surface area is the total area of all outside faces of a three-dimensional object.

Q10. What is important to understand about Nets and surface area?

Answer: Surface area is the total area of all outside faces of a three-dimensional object.

Q11. What is important to understand about Rectangular-prism surface area?

Answer: Surface area is the total area of all outside faces of a three-dimensional object.

Q12. What is important to understand about Real-life area and surface-area problems?

Answer: Area measures the amount of two-dimensional space inside a shape.

Q13. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q14. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q15. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q16. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q17. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q18. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q19. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q20. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q22. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q23. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q24. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q25. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q26. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q27. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.