Geometry and measures worksheet — GCSE Foundation

1.A cuboid measures 5 cm long (left to right), 3 cm deep (front to back) and 2 cm tall. Its front elevation is 5 cm wide by 2 cm high. Its side elevation is 3 cm wide by 2 cm high. What are the dimensions of its plan view, looking down from above?

2.The curved part of a circle's circumference, between two points on the circle, has its own name. Write down this name.

3.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.

4.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

5.A radar station is at the origin of a grid, where each unit represents 1 km. A boat is detected at the point (7, 24). Work out the boat's distance from the station, then work out how many hours it will take the boat to reach the station travelling directly towards it at 5 km per hour.

6.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

7.A triangular prism has two triangular faces and three rectangular faces. How many vertices does a triangular prism have?

8.A solid has one curved surface and two flat circular faces of equal size, one at each end. What is the name of this solid?

9.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

10.Which of these describes an obtuse angle?

11.In triangle PQR and triangle STU, PQ = ST, QR = TU and PR = SU. Write down the congruence condition that proves the two triangles are congruent.

12.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.

13.The angle between north and a cycle path is 40°, but it is measured anticlockwise from north. What is the three-figure bearing of the cycle path?

14.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

15.Work out the exact value of sin 30° + cos 60°.