Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.5: Area of Composite Figures (answers)

Section A · Multiple choice 4 marks

1. All the lines meet at right angles. What is the area of the figure?1 mark

(A) 56 cm²(B) 24 cm²(C) 36 cm²(D) 30 cm²

Answer: (C) 36 cm²Split into A and B. A: 8 × 3 = 24 cm². B: 3 × 4 = 12 cm². 24 + 12 = 36 cm².

2. A rectangular floor is 16 m by 9 m. A rug 6 m by 4 m is in the middle. What is the area of the floor not covered by the rug?1 mark

(A) 168 m²(B) 24 m²(C) 100 m²(D) 120 m²

Answer: (D) 120 m²Floor: 16 × 9 = 144 m². Rug: 6 × 4 = 24 m². 144 − 24 = 120 m².

3. All the lines meet at right angles. What is the area of the T-shape?1 mark

(A) 42 cm²(B) 72 cm²(C) 34 cm²(D) 27 cm²

Answer: (A) 42 cm²Split into A and B. A: 9 × 3 = 27 cm². B: 3 × 5 = 15 cm². 27 + 15 = 42 cm².

4. A square with sides of 10 cm is joined to a rectangle 10 cm by 6 cm. What is the total area?1 mark

(A) 120 cm²(B) 160 cm²(C) 76 cm²(D) 60 cm²

Answer: (B) 160 cm²Square: 10 × 10 = 100 cm². Rectangle: 10 × 6 = 60 cm². 100 + 60 = 160 cm².

5. All the lines meet at right angles. What is the area of the staircase figure?1 mark

Answer: 24 m²Rows are 2 m, 4 m and 6 m long, each 2 m tall. 2 × 2 + 4 × 2 + 6 × 2 = 4 + 8 + 12 = 24 m².

6. A picture frame is 18 cm by 12 cm. The window inside is 10 cm by 6 cm. What is the area of the frame (shaded part)?1 mark

Answer: 156 cm²Whole: 18 × 12 = 216 cm². Window: 10 × 6 = 60 cm². 216 − 60 = 156 cm².

7. A rectangle 12 cm by 7 cm is joined to a square with sides of 7 cm. What is the total area?1 mark

Answer: 133 cm²12 × 7 = 84 cm². 7 × 7 = 49 cm². 84 + 49 = 133 cm².

8. All the lines meet at right angles. What is the area of the figure?1 mark

Answer: 60 cm²Split into A (10 × 4 = 40 cm²) and B (4 × 5 = 20 cm²). 40 + 20 = 60 cm².

9. A square of side 8 cm is cut from a square of side 20 cm. What is the area of the shaded part?1 mark

Answer: 336 cm²20 × 20 = 400 cm². 8 × 8 = 64 cm². 400 − 64 = 336 cm².

10. A garden is 20 m by 14 m. A path 2 m wide runs all round inside the edge of the garden. What is the area of the path?2 marks

Answer: 120 m²Garden: 20 × 14 = 280 m². Inside the path: (20 − 4) × (14 − 4) = 16 × 10 = 160 m². 280 − 160 = 120 m².

11. A wall is 5 m by 3 m. A window 2 m by 1 m and a door 1 m by 2 m are not painted. What is the area that is painted?2 marks

Answer: 11 m²Wall: 5 × 3 = 15 m². Window: 2 × 1 = 2 m². Door: 1 × 2 = 2 m². 15 − 2 − 2 = 11 m².

12. All the sides are equal and all the lines meet at right angles. Each side is 4 cm. What is the area of the cross?2 marks

Answer: 80 cm²The cross is made of 5 squares, each 4 × 4 = 16 cm². 5 × 16 = 80 cm².

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