Geometry and measures worksheet — GCSE Foundation

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

2.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

3.A triangle has a base of 8 cm and a perpendicular height of 5 cm. Work out its area.

4.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

5.In a right-angled triangle one of the other two angles is 45°, and the side opposite that 45° angle is 7 cm. Work out the length of the hypotenuse. Give your answer to 1 decimal place.

6.A children's slide is built as a right-angled triangle: the vertical ladder side is 2.4 m, the horizontal base along the ground is 3.2 m, and the sloping slide is the third side. Work out the exact length of the sloping slide.

7.How many vertices does a cuboid have?

8.Two triangles are similar. The sides of the first triangle are 3 cm, 4 cm and 5 cm. The shortest side of the second triangle is 9 cm. Work out the scale factor from the first triangle to the second.

9.A fan-shaped rug is in the shape of a sector of a circle with radius 4 m and angle 180°. It costs £4 per square metre to make. Using π = 3.14, work out the total cost of the rug.

10.In quadrilateral WXYZ, which of the following correctly names the angle at vertex Y using standard notation?

11.In triangle ABC and triangle DEF, the angle at A equals the angle at D, and AB ÷ DE = AC ÷ DF. Write down what this proves about the two triangles.

12.A map has a scale of 1 cm : 5 km. A road is drawn 3 cm long on the map. What is the real length of the road?

13.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

14.Point C is at (5, 2). It is reflected in the x-axis. Work out the coordinates of the image of point C.

15.A straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.