Geometry and measures worksheet — GCSE Foundation

1.A solid has 6 faces and 8 vertices. Using the formula F + V − E = 2, work out how many edges it has.

2.A goat is tied by a rope 7 m long to a post at a corner of a rectangular field, where two fences meet at a right angle. The goat can reach anywhere inside the field that the rope allows. Using π = 3.14, work out the area the goat can graze, to the nearest square metre.

3.How many vertices does a cuboid have?

4.The midpoint of the line segment AB is (3, 5). A is the point (1, 3). Work out the coordinates of B.

5.A garden bed is designed as a trapezium. The two parallel sides are 8 m and 12 m, and the perpendicular distance between them is 5 m. Grass seed covers 4 m² per bag, sold only in whole bags. Work out how many bags of grass seed are needed.

6.A right-angled triangle has angles of 90°, 40° and x°. Work out the value of x.

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

8.A(1, 2), B(5, 2) and C(5, 6) are three of the four vertices of a square ABCD. Work out the coordinates of D.

9.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

10.Point A and point B are 5 cm apart. How many points are exactly 4 cm from A and exactly 3 cm from B?

11.Triangle T has a vertex at (2, 1). It is enlarged by a scale factor of 3, centre (0, 0). Work out the coordinates of the image of this vertex.

12.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

13.Work out the exact value of (sin 30°)² + (cos 30°)².

14.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.

15.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?