Geometry and measures worksheet — GCSE Foundation

1.The diagram shows a solid built from identical cubes. How many squares are in its plan view, the view looking straight down from above?

2.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

3.A quadrilateral has all four sides equal in length and all four interior angles equal to 90°. Its diagonals are equal in length and bisect each other at right angles. Which quadrilateral matches this description exactly?

4.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

5.In one circle, chord PQ is 6 cm long, chord RS is 10 cm long, chord TU is 14 cm long and chord VW is 15 cm long. Write down which of these chords lies closest to the centre of the circle.

6.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.

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 garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

9.A carpenter cuts two triangular metal brackets for a shelf. Bracket P has sides of 12 cm, 16 cm and 20 cm. Bracket Q has sides of 16 cm, 20 cm and 12 cm, listed in a different order. Before fitting them as a matching pair, the carpenter wants to check they are exactly the same shape and size. Which of the following correctly justifies this?

10.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

11.An isosceles trapezium has exactly one pair of parallel sides, and its two non-parallel sides are equal in length. How many lines of symmetry does it have?

12.A right-angled triangle has two sides of length 5 cm and 12 cm, and the angle between those two sides is 90°. Work out the length of the hypotenuse.

13.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

14.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

15.A furniture catalogue drawing uses a scale of 1 cm to 1.5 m. A sofa in the drawing is measured as 7 cm long. What is the real length of the sofa, in metres?