Geometry and measures worksheet — GCSE Foundation

1.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.

2.A hexagonal prism has 8 faces and 12 vertices. Using F + V − E = 2, work out how many edges it has.

3.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.

4.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

5.A ship sails 12 km on a bearing of 070° from a harbour to a buoy. It then sails a further 9 km, still on a bearing of 070°, from the buoy to a lighthouse. How far is the lighthouse from the harbour, in kilometres?

6.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

7.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

8.A designer creates a repeating tile pattern. Each tile is translated from the one before it by the column vector with top number 4.5 and bottom number −2.5 (in centimetres). The first tile has its bottom-left corner at (1.5, 3). Work out the coordinates of the bottom-left corner of the third tile.

9.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

10.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

11.A circle has a radius of 1 cm. Work out the circumference of the circle. Give your answer in terms of π.

12.A tent's sloping side makes an angle of 45° with the ground. The sloping side is 3√2 m long. Using the exact value of sin 45°, work out the exact height of the tent.

13.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

14.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

15.A rectangular garden bed measures 5 m by 3 m. A semicircular flower border is attached along one of the 3 m-wide ends, on the outside of the rectangle, so that the 3 m side is the diameter of the semicircle. Work out the total perimeter of the combined shape (the two long sides, the one remaining short side, and the curved edge). Use π = 3.14.