Geometry and measures worksheet — GCSE Higher

1.A triangle has one unknown side or angle, marked x. In which one of these situations should the sine rule, rather than the cosine rule, be used to find x?

2.In triangle ABC, AB = 9.4 cm, AC = 7.2 cm and angle BAC = 63°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.

3.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

4.Two similar hexagonal tiles have lengths in the ratio 4 : 7. A side of the smaller tile is 8.4 cm long. Work out the length of the corresponding side of the larger tile.

5.Point P has coordinates (6, 4). P is rotated 90° clockwise about the point (1, 2), and the image is then translated by the vector (−3, 5). Work out the coordinates of the final image of P.

6.ABCD is a cyclic quadrilateral, with its vertices in that order around the circle. Angle DAB = 108°. Work out the size of angle BCD.

7.A footpath sign shows a distance of 0.45 km to the next village. Work out this distance in metres.

8.Two cylindrical storage tins are geometrically similar. The smaller tin has height 4 cm and the larger tin has height 6 cm. Work out the ratio of the surface area of the smaller tin to the surface area of the larger tin, giving your answer in the form a : b in its simplest form.

9.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?

10.A cylinder has a radius of 5 cm. Its volume is 471 cm³. Using π = 3.14, work out the height of the cylinder.

11.Shape S is enlarged by a scale factor of −3 about a fixed centre. Which statement correctly describes the image compared to the original shape?

12.A triangular prism has a cross-section that is a triangle with a base of 3.5 cm and a perpendicular height of 4 cm. The prism is 10 cm long. Work out the volume of the prism.

13.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

14.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

15.Two similar signs have lengths in the ratio 9 : 4. The larger sign has a side of length 14.4 cm. Work out the length of the corresponding side of the smaller sign.