Year 4 perimeter and area worksheet answers to download as PDF

These Year 4 perimeter and area worksheet answers give a full worked solution to all 20 questions of the perimeter and area worksheet. Try each question yourself first, then check your method step by step.

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Answer to Question 1
1. 8 + 5 + 8 + 5 = 26 cm.
2. 2 × (12 + 7) = 2 × 19 = 38 m.
3. 4 × 9 = 36 cm.
4. 2 × (15 + 9) = 2 × 24 = 48 cm.
Answer to Question 2
1. The shape is 4 cm high on the right and the left side is 2 cm, so the step is 4 − 2 = 2 cm.
2. Sides: 7 + 4 + 3 + 2 + 4 + 2 = 22 cm.
3. The surrounding rectangle is 7 cm by 4 cm: 2 × (7 + 4) = 22 cm, the same.
Answer to Question 3
1. 4 rows of 6 squares: 4 × 6 = 24 cm².
2. 7 rows of 3 squares: 7 × 3 = 21 cm².
3. The bottom part has 2 rows of 5 squares: 10 squares. The top part has 2 more rows of 2 squares: 4 squares. 10 + 4 = 14 cm².
Answer to Question 4
1. 9 × 4 = 36 cm².
2. 12 × 6 = 72 m².
3. 15 × 8 = 120 cm² (10 × 8 = 80 and 5 × 8 = 40).
4. 11 × 11 = 121 m².
Answer to Question 5
1. 36 ÷ 9 = 4 cm, because 9 × 4 = 36.
2. The two widths are 5 + 5 = 10 m, so the two lengths are 34 − 10 = 24 m. One length is 24 ÷ 2 = 12 m.
3. 72 ÷ 8 = 9 m, because 8 × 9 = 72.
4. 28 ÷ 4 = 7 cm.
Answer to Question 6
1. Half of the perimeter is 12 cm, so width = 12 − length. Length 11: width 1 cm, area 11 cm². Length 9: width 3 cm, area 27 cm². Length 6: width 6 cm, area 36 cm². Table: (1 cm, 11 cm²), (3 cm, 27 cm²), (6 cm, 36 cm²).
2. The biggest area is 36 cm², for the rectangle that is 6 cm by 6 cm: it is a square.
3. 11 cm² is much smaller than 36 cm². The difference is 25 cm², even though the perimeters are the same.
Answer to Question 7
1. 2 × (14 + 9) = 2 × 23 = 46 m.
2. 46 ÷ 2 = 23 panels.
3. 23 × £18 = £414 (20 × 18 = 360 and 3 × 18 = 54).
4. A 2 m gap needs 1 panel less: 1 fewer, so 22 panels cost 22 × £18 = £396.
Answer to Question 8
1. 5 × 4 = 20 m².
2. 20 × £12 = £240.
3. The perimeter is 2 × (5 + 4) = 18 m.
4. 18 × £3 = £54.
Answer to Question 9
1. 20 × 15 = 300 cm².
2. 2 × (20 + 15) = 70 cm.
3. 70 ÷ 10 = 7, so 7 × 20p = 140p = £1.40.
4. 25 × 25 = 625 cm². Not covered: 625 − 300 = 325 cm².
Answer to Question 10
1. 40 × 25 = 1 000 m².
2. 10 × 10 = 100 m².
3. 1 000 − 100 = 900 m².
4. The perimeter is 2 × (40 + 25) = 130 m, so twice is 2 × 130 = 260 m.
Answer to Question 11
1. 3 × 2 = 6 m².
2. 6 × 4 = 24 tiles.
3. 24 ÷ 10 = 2 remainder 4, so she needs 3 boxes (30 tiles).
4. 3 × £15 = £45. Tiles left over: 30 − 24 = 6 tiles.
Answer to Question 12
1. Bed A: 8 × 3 = 24 m². Bed B: 6 × 4 = 24 m².
2. The areas are equal: neither is bigger (the difference is 0 m²).
3. Bed A: 2 × (8 + 3) = 22 m. Bed B: 2 × (6 + 4) = 20 m.
4. The areas are the same, so no bed has the bigger area. But Bed A has the bigger perimeter (22 m > 20 m). Two shapes with the same area can have different perimeters.
Answer to Question 13
1. 2 × (60 + 40) = 200 m.
2. 60 × 40 = 2 400 m².
3. 2 × (25 + 10) = 70 m.
4. 70 ÷ 5 = 14 posts.
Answer to Question 14
1. 4 × 3 = 12 m².
2. 2 × (4 + 3) = 14 m.
3. 14 × £5 = £70.
4. 12 ÷ 2 = 6 bags.
Answer to Question 15
1. 8 + 3 + 4 + 3 + 4 + 6 = 28 m. Check: surrounding rectangle 8 by 6 has perimeter 2 × 14 = 28 m.
2. Bottom rectangle: 8 × 3 = 24 m². Top rectangle: 4 × 3 = 12 m².
3. 24 + 12 = 36 m². Check: 8 × 6 − 4 × 3 = 48 − 12 = 36 m².
4. 36 × £14 = £504 (36 × 10 = 360 and 36 × 4 = 144).
5. 28 × £4 = £112.
Answer to Question 16
1. The length plus the width is 12 m. The rectangles are: 11 × 1, 10 × 2, 9 × 3, 8 × 4, 7 × 5 and 6 × 6.
2. Areas: 11 m², 20 m², 27 m², 32 m², 35 m² and 36 m².
3. Biggest: 6 m by 6 m (36 m²), a square. Smallest: 11 m by 1 m (11 m²).
4. At least 30 m²: 8 × 4 (32), 7 × 5 (35) and 6 × 6 (36).
5. 8 m long means the width is 4 m: area 8 × 4 = 32 m². £128 ÷ 32 = £4 per m².
Answer to Question 17
1. 4 × 3 = 12 m².
2. 2 × 1 = 2 m².
3. 12 − 2 = 10 m².
4. 10 ÷ 6 = 1 remainder 4, so 1 tin is not enough: he needs 2 tins.
5. 2 × £8 = £16.
Answer to Question 18
1. Field A: 90 × 40 = 3 600 m². Field B: 60 × 60 = 3 600 m².
2. They are the same: the difference is 0 m².
3. Field A: 2 × (90 + 40) = 260 m. Field B: 4 × 60 = 240 m.
4. Field B is cheaper. The difference in perimeter is 260 − 240 = 20 m, so it saves 20 × £6 = £120.
5. Both fields have an area of 3 600 m². 3 600 ÷ 100 = 36 sheep.
Answer to Question 19
1. 2 × (60 + 40) = 200 cm = 2 m.
2. 8 × 2 = 16 m.
3. 16 × £1.50 = £24.00.
4. Card: 8 × £0.80 = £6.40. Ribbon: £24.00. Total: £30.40.
5. £30.40 + £4.00 = £34.40, which is more than £25, so there is no money left: the council needs £9.40 more.
Answer to Question 20
1. Pairs of factors of 36: 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6. Perimeters: 2 × (1 + 36) = 74 cm; 2 × (2 + 18) = 40 cm; 2 × (3 + 12) = 30 cm; 2 × (4 + 9) = 26 cm; 2 × (6 + 6) = 24 cm. There are 5 rectangles: perimeters 74, 40, 30, 26 and 24 cm.
2. The smallest perimeter is 24 cm, for the 6 by 6 rectangle, which is a square.
3. He should use the 6 m by 6 m square. He needs 24 m of fence.

How to use these Year 4 perimeter and area worksheet answers

First, try every question on the worksheet without looking. Then compare your working with the solution line by line, not only the final answer. When your answer is different, find the first step that changes, because that is where the mistake is. After that, read the matching part of the perimeter and area lesson again. Finally, check that the method is secure with the quiz or the test.

Also, the Year 4 perimeter and area worksheet answers are available as a PDF, so you can mark printed work quickly. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, these Year 4 perimeter and area worksheet answers show every step, so nothing is left unexplained.