Geometry and measures worksheet — GCSE Foundation

1.A vertical flagpole casts a shadow 6 m long at the same time as a 1.2 m vertical post casts a shadow 1.8 m long. The flagpole and the post are both vertical, and the triangles formed by each object, its shadow, and the sun's ray are similar. Work out the height of the flagpole.

2.An angle measures 108°. Write down the name given to an angle of this size.

3.Two sides of a triangle are 9 cm and 15 cm long. Write down which one of these lengths is possible for the third side.

4.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

5.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

6.A tap fills a tank at a rate of 18 litres per minute. The tank holds 0.45 m³. Work out how long the tap takes to fill the tank.

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

8.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

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

10.In triangle ABC, angle ABC = 90° and angle BAC = 30°. The hypotenuse AC = 12 cm. Work out the exact length of AB.

11.Two similar triangles have lengths in the ratio 3 : 4. The perimeter of the smaller triangle is 24 cm. Work out the perimeter of the larger triangle.

12.Two angles lie on a straight line. One angle is 37°. Work out the size of the other angle.

13.Two straight lines PQ and RS cross at point O. Angle POR = 52°. Work out angle QOS.

14.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

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