Geometry and measures worksheet — GCSE Foundation

1.In quadrilateral ABCD the two sides AB and BC are each 6 cm long and meet each other at B. The two sides CD and DA are each 9 cm long and meet each other at D. No side of ABCD is parallel to any other side. Write down the mathematical name of this quadrilateral.

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

3.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

4.How many edges does a cube have?

5.A sector of a circle has an angle of 90° and an area of 78.5 cm². Using π = 3.14, work out the radius of the circle.

6.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

7.Write down the number of lines of symmetry a rhombus has.

8.A hexagonal prism lies on a table. A flat cut is made straight across it, at right angles to its length (so the cut is parallel to the two identical end faces). What shape is the cross-section?

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

10.A polygon has one more side than a heptagon. What is the polygon called?

11.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?

12.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

13.An angle is measured with a protractor as 47°. What type of angle is this?

14.Put sin 30°, tan 30° and cos 30° in order of size, starting with the smallest.

15.A circle has diameter 10 cm. Using π = 3.14, work out the circumference of the circle.