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P5 Maths Area and Perimeter Paper 3: Challenge
P5 Maths Area and Perimeter Paper 3: Challenge
Ten original items, each with an answer and a one-line explanation.
Direct answers Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check every answer and redo the wrong ones.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P5 Maths Area and Perimeter |
| Level | P5 |
02 Questions (10 items)
- FoundationHow many whole-number rectangles have an area of 36 sq cm, and what is the smallest perimeter?
- FoundationAmong rectangles with perimeter 36 cm, what is the greatest possible area?
- FoundationA 4 cm by 5 cm rectangle is cut from a corner of a 12 cm by 9 cm rectangle. Find the area and perimeter left.
- IntermediateA staircase shape has 3 steps, each 3 cm wide and 2 cm high. Find its area and perimeter.
- IntermediateAn L-shaped flower bed is a 10 m square with a 6 m square corner removed. Find its area and the fence needed.
- IntermediateA corridor is 20 m long and 1.5 m wide. Carpet costs 85 dollars per sq m. Find the total cost.
- ChallengeA square side grows from 7 cm to 10 cm. By how many sq cm does the area increase?
- ChallengeA rectangle has perimeter 50 cm and length 15 cm. If the length loses 3 cm and the width gains 3 cm, by how many sq cm does the area increase?
- ChallengeA 2 cm square is cut from each corner of a 9 cm square card. Find the area and perimeter left.
- Error redoError review: a pupil says two 6 cm by 4 cm rectangles joined into a rectangle always have perimeter 32 cm. What perimeters are possible?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5 shapes, smallest perimeter 24 cm | 36 = 1 x 36 = 2 x 18 = 3 x 12 = 4 x 9 = 6 x 6, five shapes; the square 6 x 6 gives the smallest perimeter, 24 cm. |
| 2 | 81 sq cm | Length + width = 18 cm, and the product is largest when they are closest, 9 x 9 = 81 sq cm. |
| 3 | area 88 sq cm, perimeter 42 cm | Area 108 – 20 = 88 sq cm; a corner cut leaves the perimeter unchanged at (12 + 9) x 2 = 42 cm. |
| 4 | area 18 sq cm, perimeter 30 cm | Area = three 3 x 2 rectangles = 18 sq cm; the perimeter equals the bounding rectangle, 9 cm by 6 cm, so (9 + 6) x 2 = 30 cm. |
| 5 | area 64 sq m, fence 40 m | Area 100 – 36 = 64 sq m; the notch does not change the outline, so the fence is 10 x 4 = 40 m. |
| 6 | 2550 dollars | The area is 20 x 1.5 = 30 sq m, so the cost is 30 x 85 = 2550 dollars. |
| 7 | 51 sq cm | 10 x 10 – 7 x 7 = 100 – 49 = 51 sq cm; a 3 cm longer side does not add 3 sq cm. |
| 8 | 6 sq cm more | The width is 25 – 15 = 10 cm and the area is 150 sq cm; the new 12 cm by 13 cm shape keeps the perimeter but has area 156 sq cm, which is 6 sq cm more. |
| 9 | area 65 sq cm, perimeter 36 cm | Area 81 – 4 x 4 = 65 sq cm; eight 2 cm edges go and eight come, so the perimeter stays 36 cm. |
| 10 | 32 cm or 28 cm | The area is always 48 sq cm; joined along the long side the shape is 12 x 4 with perimeter 32 cm, joined along the short side it is 6 x 8 with perimeter 28 cm. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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