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.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

3.Work out the distance between the point (0, 0) and the point (5, 12).

4.A polygon has one more side than a heptagon. What is the polygon called?

5.Triangles LMN and XYZ have LM = XY, MN = YZ and LN = XZ. Give a reason why triangle LMN is congruent to triangle XYZ.

6.A ship's radar shows a lighthouse at the point (12, −4) on a grid measured in nautical miles. The ship is at (2, 5). The ship sails along the vector that takes it directly to the lighthouse, then sails along that same vector again. Work out the ship's final position.

7.Write down which quadrant contains the point (−3, 5) when plotted on a coordinate grid.

8.Write down the name given to a quadrilateral with exactly one pair of parallel sides.

9.Write down the exact value of cos 30°.

10.Write down the exact value of tan 0°.

11.A hiker walks due west. What is the three-figure bearing for this direction?

12.Lines AB and CD are parallel. A straight line EF crosses AB at point P and crosses CD at point Q. At P, angle APE = 65°. Angle APE and angle BPQ are vertically opposite. Angle BPQ and angle PQD are co-interior (allied) angles. Work out angle PQD.

13.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

14.A scale drawing of a park uses a scale of 1 : 2000. A path is drawn 8.5 cm long on the drawing. A cyclist rides the length of the path and then rides straight back again along the same path. How far does the cyclist travel in total, in metres?

15.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.