Geometry and measures worksheet — GCSE Foundation

1.A television cable runs in a straight line from the edge of a flat roof 20 m above the ground to a bracket on a wall 5 m above the ground. The horizontal distance between the roof edge and the bracket is 15 m. Work out the length of the cable. Give your answer to 1 decimal place.

2.A sector of a circle has an angle of 150°. Work out what fraction of the circle's area the sector is.

3.A packaging designer is told a box has 6 faces, 12 edges and 8 vertices, and every face is a rectangle. To fit exactly onto a shelf, the designer needs to know whether the box must be a cube. Based only on this information, which solid must the box be?

4.A circular clock face has a radius of 9 cm. Work out the circumference of the clock face. Use π = 3.14. Give your answer to 1 decimal place.

5.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

6.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

7.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

8.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

9.A circle has a diameter of 24 cm. A sector of this circle has an angle of 90°. Using π = 3.14, work out the area of the sector.

10.Point M lies exactly halfway between point A and point B, with A, M and B all on the same straight line. Which term correctly describes point M?

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

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

13.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

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

15.A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.