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Area of compound shapes practice questions with answers

Foundation and Higher · Grade 3

A second set of area of compound shapes questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

A rectangle is 10 cm by 6 cm. A 2 cm by 2 cm rectangle is cut out of it. What is the area that is left?

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Answer: 56 cm²

  1. Whole rectangle: 10 × 6 = 60 cm².
  2. Piece cut out: 2 × 2 = 4 cm².
  • Method (1): Whole rectangle: 10 × 6 = 60 cm².
  • Accuracy (1): Answer 56 cm²

Question 2 Easy

A compound shape is a 5 cm by 6 cm rectangle joined to a 2 cm by 5 cm rectangle. What is the total area?

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Answer: 40 cm²

  1. First rectangle: 5 × 6 = 30 cm².
  2. Second rectangle: 2 × 5 = 10 cm².
  • Method (1): First rectangle: 5 × 6 = 30 cm².
  • Accuracy (1): Answer 40 cm²

Question 3 Medium

A rectangle is 12 cm by 6 cm. A 4 cm by 2 cm rectangle is cut out of it. What is the area that is left?

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Answer: 64 cm²

  1. Whole rectangle: 12 × 6 = 72 cm².
  2. Piece cut out: 4 × 2 = 8 cm².
  • Method (1): Whole rectangle: 12 × 6 = 72 cm².
  • Accuracy (1): Answer 64 cm²

Question 4 Medium

A compound shape is a 5 cm by 8 cm rectangle joined to a 2 cm by 4 cm rectangle. What is the total area?

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Answer: 48 cm²

  1. First rectangle: 5 × 8 = 40 cm².
  2. Second rectangle: 2 × 4 = 8 cm².
  • Method (1): First rectangle: 5 × 8 = 40 cm².
  • Accuracy (1): Answer 48 cm²

Question 5 Hard

A rectangle is 9 cm by 7 cm. A 2 cm by 2 cm rectangle is cut out of it. What is the area that is left?

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Answer: 59 cm²

  1. Whole rectangle: 9 × 7 = 63 cm².
  2. Piece cut out: 2 × 2 = 4 cm².
  • Method (1): Whole rectangle: 9 × 7 = 63 cm².
  • Accuracy (1): Answer 59 cm²

Question 6 Hard

A compound shape is a 5 cm by 10 cm rectangle joined to a 4 cm by 3 cm rectangle. What is the total area?

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Answer: 62 cm²

  1. First rectangle: 5 × 10 = 50 cm².
  2. Second rectangle: 4 × 3 = 12 cm².
  • Method (1): First rectangle: 5 × 10 = 50 cm².
  • Accuracy (1): Answer 62 cm²

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 13 marks

A compound shape is a 5 cm by 11 cm rectangle joined to a 2 cm by 5 cm rectangle. What is the total area?

Show answer

Answer: 65 cm²

  1. First rectangle: 5 × 11 = 55 cm².
  2. Second rectangle: 2 × 5 = 10 cm².
  3. The areas are joined, so the total is 55 + 10 = 65 cm².
  • Method (1): First rectangle: 5 × 11 = 55 cm².
  • Method (1): Second rectangle: 2 × 5 = 10 cm².
  • Accuracy (1): Answer 65 cm²

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

A compound shape is a 5 cm by 13 cm rectangle joined to a 2 cm by 4 cm rectangle. What is the total area?

  1. 73 cm²
  2. 65 cm²
  3. 119 cm²
Show answer

73 cm² The result is 73 cm².

Check 2

A rectangle is 8 cm by 8 cm. A 2 cm by 2 cm rectangle is cut out of it. What is the area that is left?

  1. 60 cm²
  2. 68 cm²
  3. 64 cm²
Show answer

60 cm² The result is 60 cm².

Check 3

A compound shape is a 5 cm by 14 cm rectangle joined to a 3 cm by 2 cm rectangle. What is the total area?

  1. 76 cm²
  2. 70 cm²
  3. 128 cm²
Show answer

76 cm² The result is 76 cm².

Check 4

A rectangle is 9 cm by 8 cm. A 4 cm by 3 cm rectangle is cut out of it. What is the area that is left?

  1. 60 cm²
  2. 84 cm²
  3. 72 cm²
Show answer

60 cm² The result is 60 cm².

Check 5

A compound shape is a 5 cm by 15 cm rectangle joined to a 4 cm by 3 cm rectangle. What is the total area?

  1. 87 cm²
  2. 75 cm²
  3. 162 cm²
Show answer

87 cm² The result is 87 cm².

Check 6

A rectangle is 10 cm by 8 cm. A 4 cm by 2 cm rectangle is cut out of it. What is the area that is left?

  1. 72 cm²
  2. 88 cm²
  3. 80 cm²
Show answer

72 cm² The result is 72 cm².

Check 7

A compound shape is a 5 cm by 16 cm rectangle joined to a 2 cm by 5 cm rectangle. What is the total area?

  1. 90 cm²
  2. 80 cm²
  3. 147 cm²
Show answer

90 cm² The result is 90 cm².

Check 8

A rectangle is 11 cm by 8 cm. A 3 cm by 2 cm rectangle is cut out of it. What is the area that is left?

  1. 82 cm²
  2. 94 cm²
  3. 88 cm²
Show answer

82 cm² The result is 82 cm².

Check 9

A compound shape is a 5 cm by 17 cm rectangle joined to a 3 cm by 4 cm rectangle. What is the total area?

  1. 97 cm²
  2. 85 cm²
  3. 168 cm²
Show answer

97 cm² The result is 97 cm².

Check 10

A rectangle is 12 cm by 8 cm. A 2 cm by 2 cm rectangle is cut out of it. What is the area that is left?

  1. 92 cm²
  2. 100 cm²
  3. 96 cm²
Show answer

92 cm² The result is 92 cm².

Check 11

A compound shape is a 5 cm by 18 cm rectangle joined to a 2 cm by 4 cm rectangle. What is the total area?

  1. 98 cm²
  2. 90 cm²
  3. 154 cm²
Show answer

98 cm² The result is 98 cm².

Check 12

A rectangle is 8 cm by 9 cm. A 4 cm by 3 cm rectangle is cut out of it. What is the area that is left?

  1. 60 cm²
  2. 84 cm²
  3. 72 cm²
Show answer

60 cm² The result is 60 cm².

Check 13

A compound shape is a 5 cm by 19 cm rectangle joined to a 3 cm by 2 cm rectangle. What is the total area?

  1. 101 cm²
  2. 95 cm²
  3. 168 cm²
Show answer

101 cm² The result is 101 cm².

Check 14

A rectangle is 9 cm by 9 cm. A 4 cm by 2 cm rectangle is cut out of it. What is the area that is left?

  1. 73 cm²
  2. 89 cm²
  3. 81 cm²
Show answer

73 cm² The result is 73 cm².

Check 15

A compound shape is a 5 cm by 20 cm rectangle joined to a 4 cm by 3 cm rectangle. What is the total area?

  1. 112 cm²
  2. 100 cm²
  3. 207 cm²
Show answer

112 cm² The result is 112 cm².

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