Geometry and measures worksheet — GCSE Higher

1.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.

2.A shape is translated by the vector (5, −3), and the image is then translated by the vector (−5, 3). Which single transformation has the same overall effect as this combination, for every point?

3.A round cake has a radius of 10 cm. Icing costs £0.02 per square centimetre. One slice of the cake is a sector with an angle of 90°. Using π = 3.14, work out the cost of icing the top of that slice, to the nearest penny.

4.A sector of a circle has radius 15 cm and angle 216°. Using π = 3.14, work out the arc length of the sector.

5.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

6.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.

7.In triangle ABC, AB = 6.4 cm, BC = 9.1 cm and AC = 12.8 cm. Work out the size of the largest angle in the triangle. Give your answer to 1 decimal place.

8.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

9.A hiker walks on a bearing of 065°. She then turns clockwise through 90° and continues walking in a straight line. What bearing is she now walking on?

10.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.

11.A triangular flower bed ABC has AB = 14 m, BC = 9 m and AC = 11 m. Work out the area of the flower bed. Give your answer to 1 decimal place.

12.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?

13.A circular pizza base has a radius of 12 cm. Work out the area of the pizza base. Use π = 3.14.

14.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.

15.A game designer places a coin at (5, 3) on a grid. The game rotates the coin 90° clockwise about the point (2, 3) each time the player presses a button, and this is applied twice in a row. Work out the coordinates of the coin after the button is pressed twice.