Geometry and measures worksheet — GCSE Foundation

1.The cross-section of a tent is an isosceles triangle. The angle at the top, between the two equal sloping sides, is 62°. The other two angles are equal to each other. Work out the size of each of those two angles.

2.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

3.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

4.A sector of a circle has radius 10 cm and angle 72°. Using π = 3.14, work out the arc length of the sector.

5.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

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

7.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

8.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

9.Three of these are rational numbers and one is irrational. Write down the one that is irrational.

10.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

11.What does the statement AB = CD mean, where A, B, C and D are all points?

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

13.An angle is measured with a protractor as 47°. What type of angle is this?

14.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

15.A chocolate bar is a prism. Its cross-section is a triangle with a base of 6 cm and a perpendicular height of 5 cm, and the bar is 12 cm long. Work out the volume of the bar.