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.
Level 1 · Warm-up
1 A cube has edges of 4 cm. What is the area of its front view? (number of cm2)
Show worked solution
The front view is a 4 cm square, so its area is 4 × 4 = 16 cm2.
2 A box is 9 cm wide, 2 cm deep and 5 cm high. What is the area of its front view? (number of cm2)
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Front view = 9 by 5, so the area is 9 × 5 = 45 cm2.
3 Name the solid whose cross-section is the same triangle all the way through.
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It is a triangular prism.
Level 2 · Core
4 A box is 8 cm wide, 3 cm deep and 5 cm high. What is the area of its top view? (number of cm2)
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Top view = 8 by 3, so the area is 8 × 3 = 24 cm2.
5 A box is 8 cm wide, 3 cm deep and 5 cm high. What is the area of its side view? (number of cm2)
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Side view = 3 by 5, so the area is 3 × 5 = 15 cm2.
6 A triangular prism stands with the triangle facing the front. The triangle is 6 cm across with a perpendicular height of 4 cm, and the prism is 10 cm long. What is the area of its front view? (number of cm2)
Show worked solution
Front view is the triangle: ½ × 6 × 4 = 12 cm2. The 10 cm length does not appear in the front view.
Level 3 · Challenge
7 A box is 12 cm wide, 4 cm deep and 7 cm high. Its front view and its top view are drawn side by side. What is the total area of those two views? (number of cm2)
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Front = 12 × 7 = 84 cm2, top = 12 × 4 = 48 cm2, total 132 cm2.
8 The front view of a box is a rectangle 10 cm by 6 cm and its side view is a rectangle 4 cm by 6 cm. What is the area of its top view? (number of cm2)
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The 6 is in both views, so the height is 6. The width is 10 and the depth is 4, so the top view is 10 × 4 = 40 cm2.
9 A triangular prism has a front view that is a triangle 8 cm across with a perpendicular height of 5 cm, and the prism is 9 cm long. What is the area of its top view? (number of cm2)
Show worked solution
The top view is a rectangle 8 cm across and 9 cm back, so its area is 8 × 9 = 72 cm2. The 5 cm height is not visible from above.