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Primary 4 Mathematics · Chapter 12 · Answers and explanations

Lesson 12.6: Word Problems: Area and Perimeter (answers)

Section A · Multiple choice 4 marks

1. A rectangular field is 40 m long and 25 m wide. A fence is built once round it. What is the length of the fence?1 mark

(A) 1000 m(B) 65 m(C) 90 m(D) 130 m
Answer: (D) 130 m2 × (40 + 25) = 2 × 65 = 130 m.

2. Square tiles with sides of 2 m cover a rectangular floor 12 m by 8 m. How many tiles are needed?1 mark

(A) 24 tiles(B) 48 tiles(C) 96 tiles(D) 20 tiles
Answer: (A) 24 tilesAlong the length: 12 ÷ 2 = 6 tiles. Along the width: 8 ÷ 2 = 4 tiles. 6 × 4 = 24 tiles. Check with area: 96 ÷ 4 = 24.

3. A rectangle is 16 cm by 8 cm. A square has the same perimeter. What is the length of a side of the square?1 mark

(A) 24 cm(B) 12 cm(C) 16 cm(D) 8 cm
Answer: (B) 12 cmPerimeter = 2 × (16 + 8) = 48 cm. Side = 48 ÷ 4 = 12 cm.

4. A rectangle is 25 cm by 4 cm. A square has the same area. What is the length of a side of the square?1 mark

(A) 29 cm(B) 50 cm(C) 10 cm(D) 100 cm
Answer: (C) 10 cmArea = 25 × 4 = 100 cm². 10 × 10 = 100, so the side is 10 cm.

Section B · Write your answer 11 marks

5. A garden is 40 m by 25 m. A pond 10 m by 8 m is in the garden. The rest is grass. What is the area of the grass?1 mark

Pond40 m25 m
Answer: 920 m²Garden: 40 × 25 = 1000 m². Pond: 10 × 8 = 80 m². 1000 − 80 = 920 m².

6. A rectangle has a perimeter of 60 m and a breadth of 12 m. What is its length?1 mark

Answer: 18 mLength + breadth = 30 m. Length = 30 − 12 = 18 m.

7. A square garden has sides of 15 m. How much fencing is needed to go round it?1 mark

Answer: 60 m4 × 15 = 60 m.

8. All the lines meet at right angles. What is the area of the L-shaped garden?1 mark

AB20 m6 m8 m8 m
Answer: 184 m²A: 20 × 6 = 120 m². B: 8 × 8 = 64 m². 120 + 64 = 184 m².

9. A rectangular garden has an area of 126 m² and a length of 14 m. What is its breadth?1 mark

Answer: 9 m126 ÷ 14 = 9 m.

10. A rectangular room 8 m by 5 m is covered with carpet. Carpet costs $12 per square metre. How much does the carpet cost?2 marks

Answer: $480Area = 8 × 5 = 40 m². Cost = 40 × 12 = $480.

11. A rectangular pool is 25 m by 10 m. A path 2 m wide goes all round the outside of the pool. What is the area of the path?2 marks

Answer: 156 m²Pool and path together: (25 + 4) × (10 + 4) = 29 × 14 = 406 m². Pool: 25 × 10 = 250 m². 406 − 250 = 156 m².

12. All the lines meet at right angles. A fence is built round this L-shaped garden. Fencing costs $4 per metre. How much does the fencing cost?2 marks

20 m6 m8 m8 m
Answer: $272The perimeter equals a rectangle 20 m by 14 m: 2 × (20 + 14) = 68 m. Cost = 68 × 4 = $272.
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