Primary 4 Mathematics · Chapter 12 · Answers and explanations
Chapter 12 Revision Paper: Area and Perimeter (answers)
Section A · Multiple choice 10 marks
1. Each square is 1 cm by 1 cm. What is the perimeter of the shaded figure?1 mark
(A) 6 cm(B) 14 cm(C) 12 cm(D) 16 cm
Answer: (B) 14 cmCount the unit lengths all the way round the edge of the figure: there are 14 of them, so the perimeter is 14 cm. (Counting the 6 squares gives the area, not the perimeter.)
2. A rectangular swimming pool is 15 m long and 8 m wide. What is its perimeter?1 mark
(A) 120 m(B) 23 m(C) 46 m(D) 38 m
Answer: (C) 46 mPerimeter = 15 + 8 + 15 + 8 = 46 m. Do not multiply: 15 × 8 = 120 is the area. Do not forget a side: 15 + 8 + 15 = 38 is only three sides.
3. A square has a perimeter of 52 cm. What is the length of one side?1 mark
(A) 26 cm(B) 208 cm(C) 48 cm(D) 13 cm
Answer: (D) 13 cmA square has 4 equal sides. Side = 52 ÷ 4 = 13 cm.
4. A square has an area of 121 cm². What is its perimeter?1 mark
(A) 44 cm(B) 484 cm(C) 22 cm(D) 11 cm
Answer: (A) 44 cmFind the side first: 11 × 11 = 121, so the side is 11 cm. Perimeter = 4 × 11 = 44 cm.
5. A rectangle has an area of 144 m² and a breadth of 9 m. What is its length?1 mark
(A) 135 m(B) 16 m(C) 1296 m(D) 25 m
Answer: (B) 16 mLength = area ÷ breadth = 144 ÷ 9 = 16 m.
6. A rectangle has a perimeter of 54 cm and a length of 17 cm. What is its breadth?1 mark
7. All the lines meet at right angles. What is the perimeter of the figure?1 mark
(A) 25 cm(B) 69 cm(C) 36 cm(D) 40 cm
Answer: (D) 40 cmThe missing sides are 6 cm (top inner step) and 9 cm (left side). The perimeter equals a rectangle 11 cm by 9 cm: 2 × (11 + 9) = 40 cm. Adding only the labelled sides gives 25 cm, which is too small.
8. A square of side 5 cm is cut out of a rectangular card 18 cm by 11 cm. What is the area of the shaded part?1 mark
9. All the lines meet at right angles. What is the area of the T-shape?1 mark
(A) 120 cm²(B) 72 cm²(C) 96 cm²(D) 52 cm²
Answer: (B) 72 cm²Split into A and B. A: 12 × 4 = 48 cm². B: 4 × 6 = 24 cm². 48 + 24 = 72 cm².
10. Square tiles with sides of 2 m cover a rectangular floor 14 m by 6 m. How many tiles are needed?1 mark
(A) 84 tiles(B) 42 tiles(C) 21 tiles(D) 20 tiles
Answer: (C) 21 tilesAlong the length: 14 ÷ 2 = 7 tiles. Along the width: 6 ÷ 2 = 3 tiles. 7 × 3 = 21 tiles. Check with area: 84 ÷ 4 = 21.
Section B · Short answers 4 marks
11. A rectangle is 24 cm long and 15 cm wide. What is its area?1 mark
Answer: 360 cm²24 × 15 = 360 cm².
12. A square has an area of 169 m². What is the length of one side?1 mark
Answer: 13 m13 × 13 = 169, so each side is 13 m.
13. All the lines meet at right angles. What is the perimeter of the figure?1 mark
Answer: 32 cmSlide the steps to the edges. The perimeter equals a rectangle 8 cm by 8 cm: 4 × 8 = 32 cm. (The two bottom sides are 8 cm each because 4 + 4 = 8.)
14. All the lines meet at right angles. What is the area of the figure?1 mark
Answer: 112 cm²Split into A and B. A: 14 × 5 = 70 cm². B: 6 × 7 = 42 cm². 70 + 42 = 112 cm².
Section C · Show your working 16 marks
15. A rectangle has an area of 135 cm² and a length of 15 cm. What is its perimeter?2 marks
16. A wire 84 cm long is bent to form a square. What is the area of the square?2 marks
Answer: 441 cm²Side = 84 ÷ 4 = 21 cm. Area = 21 × 21 = 441 cm².
17. The length of a rectangle is 4 times its breadth. Its perimeter is 70 cm. Find its area.2 marks
Answer: 196 cm²Length + breadth = 70 ÷ 2 = 35 cm = 5 units. 1 unit = 35 ÷ 5 = 7 cm, so breadth = 7 cm and length = 4 × 7 = 28 cm. Area = 28 × 7 = 196 cm².
18. All the lines meet at right angles. A rectangle 20 cm by 12 cm has a notch cut out of one side. What is the perimeter of the figure?2 marks
Answer: 74 cmThe rectangle alone has a perimeter of 2 × (20 + 12) = 64 cm. The notch removes 6 cm of the top edge but adds 5 + 6 + 5 = 16 cm, so the perimeter grows by 10 cm. 64 + 10 = 74 cm. (Or add every side: 7 + 5 + 6 + 5 + 7 + 12 + 20 + 12 = 74 cm.)
19. A rectangular garden is 24 m by 15 m. A path 2 m wide runs all round inside the edge of the garden, as shown. The path is shaded. What is the area of the path?2 marks
Answer: 140 m²Garden: 24 × 15 = 360 m². The grass is 4 m shorter each way: (24 − 4) × (15 − 4) = 20 × 11 = 220 m². Path: 360 − 220 = 140 m².
20. A hall floor is 12 m by 9 m. It is covered with square carpet tiles with sides of 3 m. Each tile costs $20. How much do all the tiles cost?2 marks
Answer: $240Along the length: 12 ÷ 3 = 4 tiles. Along the width: 9 ÷ 3 = 3 tiles. Number of tiles = 4 × 3 = 12. Cost = 12 × $20 = $240.
21. The length of a rectangle is 6 cm more than its breadth. Its perimeter is 52 cm. Find its area.2 marks
Answer: 160 cm²Length + breadth = 52 ÷ 2 = 26 cm. Take away the extra 6 cm: 26 − 6 = 20 cm is 2 equal breadths, so breadth = 10 cm. Length = 10 + 6 = 16 cm. Area = 16 × 10 = 160 cm².
22. A square has a perimeter of 48 cm. It is cut into 2 identical rectangles. The 2 rectangles are then placed side by side, end to end, to make one long rectangle. What is the perimeter of the long rectangle?2 marks
Answer: 60 cmSide of the square = 48 ÷ 4 = 12 cm. Each small rectangle is 12 cm by 6 cm. Placed end to end along the 6 cm sides, they make a rectangle 12 + 12 = 24 cm long and 6 cm wide. Perimeter = 2 × (24 + 6) = 60 cm.
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