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 Find the surface area of this closed box.
Show worked solution
Faces 10 × 3 = 30, 10 × 2 = 20 and 3 × 2 = 6. SA = 2(30 + 20 + 6) = 112 cm2. 56 cm2 forgets to double; 60 cm2 is the volume; 224 cm2 doubles twice.
2 A closed box is 12 cm long, 5 cm wide and 4 cm high. Find the area of each pair of faces, then the total surface area.
Show worked solution
Top and bottom: 2 × 60 = 120. Front and back: 2 × 48 = 96. Ends: 2 × 20 = 40. Total: 120 + 96 + 40 = 256 cm2.
3 A cube has edges 9 cm long. Find its surface area in cm2.
Show worked solution
One face is 9 × 9 = 81 cm2, and there are 6 faces: 6 × 81 = 486 cm2.
Level 2 · Core
4 The ends of this prism are isosceles triangles with base 18 cm and height 12 cm. The prism is 10 cm long. Find its surface area.
Show worked solution
Slant2 = 92 + 122 = 225, so the slant is 15. Ends: 2 × ½ × 18 × 12 = 216. Base: 18 × 10 = 180. Slopes: 2 × 15 × 10 = 300. Total 696 cm2. 636 cm2 uses the height 12 instead of the slant 15; 516 cm2 leaves out the base; 912 cm2 forgets the ½ on the triangles.
5 A box with no lid is made from card. Its base is 15 cm by 10 cm and it is 6 cm high. How much card does it use? How much would it use with a lid added?
Show worked solution
Base 150, sides 2 × 90 = 180, ends 2 × 60 = 120, so the open box uses 450 cm2. The lid adds another 150: 600 cm2.
6 A closed box has a base 10 cm by 4 cm and a surface area of 192 cm2. Find its height in cm.
Show worked solution
Top and bottom: 2 × 40 = 80. The sides: 192 − 80 = 112 = 28 × h, since the perimeter of the base is 28. So h = 4. Check: 2(40 + 40 + 16) = 192 ✓.
Level 3 · Challenge
7 Three statements:
1 A cube with 5 cm edges and no lid has a surface area of 125 cm2.
2 An 8 × 4 × 2 box has the same volume as a 4 × 4 × 4 cube but a larger surface area.
3 Two 4 × 3 × 2 boxes glued together along their 4 × 3 faces make a solid with surface area 104 cm2.
Which statements are correct?
1 A cube with 5 cm edges and no lid has a surface area of 125 cm2.
2 An 8 × 4 × 2 box has the same volume as a 4 × 4 × 4 cube but a larger surface area.
3 Two 4 × 3 × 2 boxes glued together along their 4 × 3 faces make a solid with surface area 104 cm2.
Which statements are correct?
Show worked solution
Five faces of 25: 5 × 25 = 125 (1 ✓). Both volumes are 64, and the box has SA 2(32 + 16 + 8) = 112, more than the cube's 96 (2 ✓). Each box has SA 2(12 + 8 + 6) = 52, but the two glued 4 × 3 faces are hidden: 104 − 24 = 80, not 104 (3 ✗). 1 and 2.
8 The ends of this prism are right-angled triangles with hypotenuse 20 cm and one shorter side 12 cm. Its total surface area is 672 cm2. Find the third side of the triangle and the length of the prism.
Show worked solution
202 − 122 = 400 − 144 = 256, so the third side is 16 cm. Triangles: 2 × ½ × 12 × 16 = 192. Rectangles: 672 − 192 = 480 = (12 + 16 + 20) × length = 48 × length, so the length is 10 cm.
9 A toy tent has no floor. Its ends are isosceles triangles with base 16 cm and sloping sides 17 cm, and it is 10 cm long. How much fabric does it use, in cm2?
Show worked solution
Height2 = 172 − 82 = 289 − 64 = 225, so the height is 15. Ends: 2 × ½ × 16 × 15 = 240. Sloping sides: 2 × 17 × 10 = 340. No floor, so the fabric is 240 + 340 = 580 cm2.