Geometry and measures worksheet — GCSE Foundation

1.A circle has a diameter of 4 cm. Work out the radius of the circle.

2.A solid cylinder is lying on its curved side on a table, with its circular ends facing left and right. What shape is its plan view, looking down from above?

4.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

5.How many faces does a cuboid have?

6.A tile is described as having two pairs of parallel sides, four equal sides, and diagonals that cross at right angles but are not equal in length. Give a reason why this tile cannot be a square.

7.A sector of a circle has radius 8 cm and takes up three-quarters of the full circle. Work out the perimeter of the sector, in terms of π.

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

9.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

10.Work out the distance between the points (−3, 4) and (5, −2).

11.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.

12.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?

13.Write down the exact value of tan 45°.

14.Write down the mathematical name for a quadrilateral that has exactly one pair of parallel sides.

15.A ship's radio can be heard up to 30 km from the ship. A lighthouse's light can be seen up to 20 km from the lighthouse. The ship and the lighthouse are 40 km apart along the coast. Describe the region where BOTH the radio can be heard AND the light can be seen.