Geometry and measures worksheet — GCSE Foundation

1.A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.

2.Two similar ponds have perimeters in the ratio 4 : 11. The perimeter of the larger pond is 88 m. Work out the perimeter of the smaller pond.

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.Line 1 passes through (0, 1) and (2, 5). Line 2 passes through (3, 2) and (5, 6). Work out the gradient of each line. Then write down whether the two lines are parallel.

5.A triangular badge has two sides of length 8 cm and a third side of length 5 cm. Work out the perimeter of the badge.

6.Point E is at (4, 2). It is rotated 180° about the point (1, 1). Work out the coordinates of the image of point E.

7.A polygon has 9 sides. What is the name of this polygon?

8.A solid is a single cube. Its plan view (from above), front elevation (from the front) and side elevation (from the side) are drawn separately. What shape is each of these three views?

9.A garden designer describes a flower bed as a shape with four straight sides: exactly one pair of sides is parallel, those two parallel sides are different lengths, and the other two sides are equal in length to each other but not parallel to each other. Which shape should the designer draw?

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

11.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

12.A landscaper marks out two triangular flower beds using stakes and a tape measure. Bed 1 has two edges of 5 m and 7 m, meeting at a corner with a marked angle of 60° between them. Bed 2 has edges of 5 m and 7 m, meeting at a corner also marked at 60° between them. The landscaper wants to check the two beds will be exactly the same size and shape using only these three measurements. Which condition proves the two beds are congruent?

13.A tank holds 3.2 m³ of water. Work out this volume in litres.

14.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

15.A circle has centre O. Radii OA and OB are drawn, together with the arc AB, enclosing a sector. The straight chord AB is also drawn. Write down the name of the region enclosed between the chord AB and the arc AB.