Geometry and measures worksheet — GCSE Foundation

1.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.

2.A shop stacks tins in a display block. The front elevation of the block is 4 tins wide and 3 tins high. The side elevation shows the block is 2 tins deep. Every position in the block is filled. How many tins are used in total?

3.A sector of a circle has radius 6 cm and an area of 4.71 cm². Using π = 3.14, work out the angle of the sector.

4.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

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

6.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

7.A trapezium has parallel sides of 5.6 cm and 8.4 cm, and a perpendicular height of 4 cm. Work out the area of the trapezium.

8.A line segment joins A(1, 1) and B(4, 7). Write down the sign of the gradient of this line.

9.In a right-angled triangle, the two shorter sides are a and b, and the hypotenuse is c. Write down the correct statement of Pythagoras' theorem.

10.A car's windscreen wiper blade is 40 cm long and sweeps through an angle of 110° as it wipes the glass. Using π = 3.14, work out the area of glass it wipes, to the nearest cm².

11.Write down the exact value of sin 60°.

12.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

13.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.

14.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

15.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.