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 area of a right-angled triangle with base 10 cm and height 6 cm?
Show worked solution
10 × 6 ÷ 2 = 30 cm2.
2 A parallelogram has base 7 cm and height 4 cm. Give the area of the rectangle it rearranges into, and so the area of the parallelogram.
Show worked solution
Rectangle 7 × 4 = 28; the parallelogram is the same 28 cm2.
3 What is the area of a triangle with base 8 cm and height 8 cm, in cm2?
Show worked solution
64 ÷ 2 = 32 cm2.
Level 2 · Core
4 What is the area of this triangle? Its base is 12 and its height is 5.
Show worked solution
12 × 5 ÷ 2 = 30.
5 A parallelogram has base 9 cm, height 5 cm and slanted sides of 6 cm. Give its area and its perimeter.
Show worked solution
Area 9 × 5 = 45 cm2. Perimeter 2 × (9 + 6) = 30 cm.
6 A square of side 8 cm is cut along a diagonal into two triangles. What is the area of each triangle, in cm2?
Show worked solution
64 ÷ 2 = 32 cm2.
Level 3 · Challenge
7 A parallelogram has base 7, height 4 and slanted side 4.5.1 Its area is 28.
2 Its perimeter is 23.
3 Its area is 31.5.
Which statements are correct?
2 Its perimeter is 23.
3 Its area is 31.5.
Which statements are correct?
Show worked solution
7 × 4 = 28 (1 ✓). 2 × 11.5 = 23 (2 ✓). 31.5 uses the slanted side as the height (3 ✗). 1 and 2.
8 A trapezium is 10 along the bottom, 6 along the top, and 4 high. Split it into a 6 by 4 rectangle and two right-angled triangles. Give the area of the rectangle, of ONE triangle, and of the whole trapezium.
Show worked solution
Rectangle 6 × 4 = 24. Each triangle 2 × 4 ÷ 2 = 4. Total 24 + 4 + 4 = 32.
9 A triangle has an area of 30 cm2 and a base of 12 cm. What is its height, in cm?
Show worked solution
12 × height = 60, so the height is 5 cm.