Geometry and measures worksheet — GCSE Foundation

1.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

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

3.A trapezium has parallel sides of length 6 cm and 10 cm, and a perpendicular height of 4 cm. Work out its area.

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

5.A sector of a circle has radius 7 cm and angle 90°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.

6.A survey team measures the angle between two fences with a protractor and gets a reading of 254°. What type of angle is this?

7.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

8.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

9.Write down the term for the distance all the way around the edge of a circle.

10.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

11.A plumber charges a £45 call-out fee, plus £28 for each hour worked. She works on a job for 3 hours 30 minutes, and her hours are billed by rounding up to the next whole hour. Work out the total amount she charges.

12.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

13.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

14.In a right-angled triangle, the side opposite angle θ is 6 cm and the hypotenuse is 10 cm. Work out the size of angle θ. Give your answer correct to 1 decimal place.

15.A quadrilateral has both pairs of opposite sides parallel and equal in length, but none of its angles are right angles. Which statement about this quadrilateral is correct?