Geometry and measures worksheet — GCSE Higher

1.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

2.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

3.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

4.A builder props a straight plank against a vertical wall to reach a window ledge. The foot of the plank is 2.1 m from the base of the wall, and the plank is 3.5 m long. Work out how high up the wall the plank reaches.

5.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

6.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

7.A student is proving that opposite angles of a cyclic quadrilateral ABCD sum to 180°, letting a = angle DAB and c = angle BCD, and using the fact that the angle at the centre is twice the angle at the circumference. She has already written: 'By the angle at the centre theorem, the reflex angle BOD equals 2a and the non-reflex angle BOD equals 2c.' Which statement must come immediately after this one in a correct proof?

8.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.

9.A, B and C are points on a circle with centre O. B is on the major arc AC. Angle AOC = 116°. Work out the size of angle ABC.

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

11.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

12.In triangle OAB, OA = a and OB = b. M is the midpoint of OA, and N is the midpoint of OB. Express the vector MN in terms of a and b.

13.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.

14.A vertical line passes through the point (5, 2). Write down the equation of this line.

15.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?