Shape and Space: Further Practice

Surface area, a missing Pythagorean leg, and a composite figure's area.

8 questions, free, marked as you go with a worked explanation on every one.

What this covers

• right triangles and circles

The questions

1. A right triangle has a hypotenuse of 13 cm and one leg of 5 cm. Find the length of the other leg, in centimetres.
2. Find the surface area of a cube with side length 6 cm, in square centimetres.
3. A rectangular prism has length 4 cm, width 3 cm, and height 5 cm. Find its surface area, in square centimetres.
4. A figure is made of a rectangle 10 cm by 6 cm with a semicircle of radius 3 cm attached to one of its short ends. Find the total area of the figure, to the nearest whole number, in square centimetres. (Use π ≈ 3.14.)
5. A cylinder has radius 4 cm and height 9 cm. Find its total surface area, to the nearest whole number, in square centimetres. (Use total surface area = 2πr² + 2πrh and π ≈ 3.14.)
6. A rectangular television screen measures 48 cm by 27 cm. Find the length of its diagonal, to the nearest whole number, in centimetres.
7. A right triangle has a hypotenuse of 17 cm and one leg of 8 cm. Find the length of the other leg, in centimetres.
8. Which set of three side lengths could NOT form a right triangle?

Answer these free