Geometry and measures worksheet — GCSE Foundation

1.A stained-glass window panel is designed as a kite. Two adjacent sides are each 25 cm, and the other two adjacent sides are each 40 cm. A frame is fitted around the whole panel. The frame costs £2.50 per metre, sold only in whole metres. Work out the total cost of the frame.

2.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

3.Lines GH and JK are parallel. A straight line crosses GH at point M and crosses JK at point N. Angle HMN = 71°. Angle HMN and angle MNK are alternate angles. Work out angle MNK.

4.Write down the exact value of cos 45°.

5.A rectangular garden gate is 3 m wide and 4 m high. A straight brace runs from one corner of the gate to the opposite corner. Work out the length of the brace.

6.How many vertices does a square-based pyramid have?

7.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

8.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

9.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.

10.Write down the exact value of tan 60°.

11.A translation moves the point (1, 1) to the point (9, 4). Write down the column vector of this translation.

12.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

13.Which of the following is the correct definition of a regular polygon?

14.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

15.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.