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 has an area of 48 cm2 and a width of 6 cm. What is its length?
Show worked solution
48 ÷ 6 = 8 cm.
2 Rectangle P is 12 by 3. Give its area, and the length of a rectangle with the same area that is 4 wide.
Show worked solution
Area 36. 36 ÷ 4 = 9.
3 A square has an area of 49 cm2. What is the length of one side, in cm?
Show worked solution
7 × 7 = 49, so 7 cm.
Level 2 · Core
4 What is the area of a rectangle that is 4 units long and 1½ units high?
Show worked solution
4 × 1½ = 6.
5 List the rectangles with whole-number sides and area 24: give the perimeter of the 4 by 6 one and of the 1 by 24 one.
Show worked solution
20 and 50. Same area, very different perimeters.
6 A rectangle 12 cm by 3 cm is cut up and rearranged into a square. What is the side of the square, in cm?
Show worked solution
12 × 3 = 36 = 6 × 6, so 6 cm.
Level 3 · Challenge
7 A rectangle has an area of 36 cm2.1 It could be 4 cm by 9 cm.
2 If it is 4 by 9, its perimeter is 26 cm.
3 Every rectangle with area 36 has perimeter 26.
Which statements are correct?
2 If it is 4 by 9, its perimeter is 26 cm.
3 Every rectangle with area 36 has perimeter 26.
Which statements are correct?
Show worked solution
4 × 9 = 36 (1 ✓). 2 × 13 = 26 (2 ✓). A 6 by 6 has area 36 and perimeter 24 (3 ✗). 1 and 2.
8 A rectangle has a perimeter of 26 cm and an area of 40 cm2. Give its two sides, shorter first.
Show worked solution
5 and 8: 5 + 8 = 13, 5 × 8 = 40.
9 A rectangle 15 cm long has the same area as a 10 cm by 6 cm rectangle. What is its width, in cm?
Show worked solution
60 ÷ 15 = 4 cm.