Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 What is the perimeter of an 8 cm by 3 cm rectangle?
Show worked solution
2 × 11 = 22 cm.
2 Give the perimeter of a square with side 7 cm, and of a 9 cm by 4 cm rectangle.
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Square 28 cm. Rectangle 2 × 13 = 26 cm.
3 A rectangle has a perimeter of 30 cm and a width of 5 cm. What is its length, in cm?
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15 − 5 = 10 cm.
Level 2 · Core
4 This L-shape is 6 cm wide and 5 cm tall. What is its perimeter?
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2 × (6 + 5) = 22 cm.
5 In this L-shape the bottom is 10, the left side is 8, the top piece is 4 and the short right piece is 3. Find the two unlabelled sides.
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10 − 4 = 6; 8 − 3 = 5.
6 The perimeter of a square is 36 cm. What is the length of one side, in cm?
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36 ÷ 4 = 9 cm.
Level 3 · Challenge
7 This shape is 10 wide and 8 tall with a notch 3 deep cut into the top.1 Its perimeter is 42.
2 Its perimeter is greater than that of a 10 by 8 rectangle.
3 Its perimeter is 36.
Which statements are correct?
2 Its perimeter is greater than that of a 10 by 8 rectangle.
3 Its perimeter is 36.
Which statements are correct?
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36 + 2 × 3 = 42 (1 ✓), which is more than 36 (2 ✓, 3 ✗). 1 and 2.
8 A rectangle is 20 cm long and has a perimeter of 64 cm. Find its width. Two such rectangles joined along a short side make a 40 cm long rectangle — find its perimeter.
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20 + w = 32, so w = 12. New: 2 × (40 + 12) = 104 cm — which is 64 + 64 − 2 × 12.
9 A rectangle has a perimeter of 80 cm and its length is 3 times its width. What is the width, in cm?
Show worked solution
8w = 80, so w = 10 cm (length 30).