Geometry and measures worksheet — GCSE Foundation

1.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.

2.Which of these describes an obtuse angle?

3.Triangle T has a vertex at (8, 4). It is enlarged by a scale factor of 1/2, centre (2, 4). Work out the coordinates of the image of this vertex.

4.In geometry, which of the following best describes a 'plane'?

5.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

6.A sector has an angle of 45°. Priti says: 'The area of the sector is one eighth of the area of the full circle, whatever the radius is.' Is Priti correct?

7.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

8.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

9.Triangle JKL has a right angle at K, hypotenuse JL = 13 cm, and side JK = 5 cm. Triangle MNO has a right angle at N, hypotenuse MO = 13 cm, and side MN = 5 cm. Using only the facts given, and without working out any further lengths, write down the congruence condition that proves triangle JKL is congruent to triangle MNO.

10.A rhombus has all four sides equal in length. Write down how many pairs of parallel sides a rhombus has.

11.In quadrilateral ABCD, side AB is parallel to side DC. Which statement correctly uses geometric notation to show this?

12.A triangular bunting flag has two equal sides. The angle between those two equal sides is 80°, and the other two angles of the flag are equal to each other. Work out the size of each of the two equal angles.

13.A circle has two straight radii drawn from the centre to the edge, together with the arc between them. Write down the name of the region enclosed by these two radii and the arc.

14.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.

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