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 A rectangle is 12 cm by 5 cm. What is its area, in square centimetres?
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60 square centimetres.
2 An L-shape fits inside a rectangle 7 units wide and 5 units tall. Write the missing across side and the missing up side.
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3 across and 2 up.
3 A rectangle has an area of 60 cm² and is 4 cm wide. How many centimetres long is it?
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15 cm.
Level 2 · Core
4 What is the perimeter of this L-shape, in units?
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2 × (7 + 5) = 24 units.
5 Write the area of the ring between a 5 by 5 square and a 4 by 4 square, and the area of the ring between the 4 by 4 and the 3 by 3.
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9 and 7 squares.
6 A rectangle has a perimeter of 30 cm and one side of 9 cm. How many centimetres is the other side?
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6 cm.
Level 3 · Challenge
7 Two identical rectangles, each 5 cm by 3 cm, are joined along a 3 cm side.1 The new shape is 10 cm by 3 cm.
2 Its area is 30 cm².
3 Its perimeter is 32 cm.
Which statements are correct?
2 Its area is 30 cm².
3 Its perimeter is 32 cm.
Which statements are correct?
Show worked solution
Side by side they make 10 by 3 (1 ✓) with area 30 cm2 (2 ✓). The perimeter is 2 × (10 + 3) = 26, not 32, because the two joined edges are now inside (3 ✗). 1 and 2.
8 Rectangle P is 12 cm by 5 cm. Rectangle Q has the same area and is 4 cm wide. Write P's area and Q's length.
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60 cm2, and 60 ÷ 4 = 15 cm.
9 A rectangle is w cm by 6 cm. An identical one is joined along a 6 cm side, and the perimeter grows by 16 cm. What is w?
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2w = 16, so w = 8 cm.