Geometry and measures worksheet — GCSE Foundation

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

2.In a right-angled triangle, θ is one of the acute angles. Write down the trigonometric ratio, in terms of the opposite and adjacent sides, that is used to find θ.

3.A room measures 4.2 m by 3.6 m. A flooring company needs the area in cm² to order the right amount of vinyl flooring. Work out the area of the room in cm².

4.A ladder rests against a wall, making an angle of 60° with the ground. The ladder is 2 m long. Using the exact value of sin 60°, work out how high up the wall the ladder reaches, giving your answer in centimetres.

5.A cube has all of its edges the same length. How many planes of symmetry does it have?

6.Two triangles are congruent to each other. What does this tell you about their angles and sides?

7.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

8.A model car is built to a scale of 1 : 24. The real car is 4.32 m long. Work out the length of the model, in centimetres.

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

10.To construct the perpendicular from a point P to a line l, where P is a point above l, an arc centred at P is drawn to cross l at two points, X and Y. What is the correct next step?

11.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

12.m is the column vector with top number 4 and bottom number 6. n is the column vector with top number −6 and bottom number −9. Given that n = k × m for some number k, work out the value of k.

13.Write down the exact value of tan 45°.

14.How many edges does a triangular prism have?

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