Geometry and measures worksheet — GCSE Higher

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

2.A support strut for a shed roof is in the shape of a right-angled triangle. The two shorter sides of the strut are 5 m and 9 m. Work out the length of the sloping strut (the hypotenuse). Give your answer correct to 1 decimal place.

3.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

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

5.A right-angled triangle has a hypotenuse of 10 cm. One of its other angles is 45°. Work out the exact length of one of the two shorter sides.

6.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.

7.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

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

9.A zip wire is fixed at an angle of 50° to the horizontal, running from a high platform down to the ground. The zip wire itself, from the platform to the ground, is 12 m long. Work out the horizontal distance covered by the zip wire. Give your answer correct to 1 decimal place.

10.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.

11.A solid metal sphere has a radius of 5 cm. It is melted down and recast into a solid cylinder with the same radius, 5 cm. Work out the height of the cylinder, so that its volume equals the volume of the sphere. Use π = 3.14 and give your answer correct to 1 decimal place.

12.In triangle ABC, AB = 9 cm, AC = 6 cm, and angle BAC = 65°. Work out the length of BC. Give your answer to 1 decimal place.

13.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.

14.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

15.A field ABCD is a convex quadrilateral. AB = 40 m, BC = 32 m and angle ABC = 95°. The other two sides are CD = 25 m and DA = 36 m. Work out the area of the field. Give your answer to the nearest square metre.