Geometry and measures worksheet — GCSE Foundation

1.A garden flower bed is in the shape of a trapezium. Its two parallel edges are 3.5 m and 6.5 m long, and the perpendicular distance between them is 4 m. Bedding plants cost £2.50 per square metre to cover the bed. Work out the total cost of the bedding plants.

2.A straight line is drawn from the centre of a circle to a point on the circle. Write down the name of this line.

3.A rectangle has vertices at (2, 1), (9, 1), (9, 5) and (2, 5). Work out the area of the rectangle.

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

5.A roof has two triangular sections, P and Q. Section P has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them. Section Q has a sloping edge of 3.6 m and a base edge of 2.4 m, with an angle of 70° between them, arranged the same way round. A roofer wants to cut identical triangular felt panels for both sections without measuring Section Q separately. Which condition confirms that the two sections are congruent?

6.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

7.In triangle XYZ, the side opposite vertex X is labelled using the standard lowercase-letter convention. Which label is correct?

8.A cyclist's journey from her house to the shop is represented by the column vector with top number 2 and bottom number 5, where each unit is 1 km east and 1 km north. She then cycles from the shop to the park, represented by the column vector with top number 4 and bottom number −3. What single column vector represents her journey from her house directly to the park?

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

10.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.

11.A kite string makes an angle of 30° with the ground. The kite is flying at a height of 6 m directly above a point on the ground. Using the exact value of sin 30°, work out the exact length of the kite string.

12.For two triangles to be proved congruent using SAS, which two facts must be true about both triangles?

13.Priya says: 'To find the arc length of a sector, you divide the circumference by the angle in degrees.' Which statement about Priya's method is correct?

14.Two triangles are proved congruent using the ASA condition. What can be concluded about the two remaining pairs of corresponding sides that were not part of the original ASA facts?

15.A jug holds 750 ml of water. Work out what fraction of a litre this is.