Geometry and measures worksheet — GCSE Foundation

1.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?

2.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

3.A cylindrical water tank has a solid hemispherical dome on top, both with radius 2 m. Work out the volume of the hemispherical dome alone. Use π = 3.14 and give your answer correct to 3 decimal places.

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 sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)

6.A triangular flag has a base of 40 cm and a perpendicular height of 25 cm. Work out its area.

7.A solid has 4 triangular faces, 4 vertices and 6 edges. What is the name of this solid?

8.Point D is at (3, 7). It is reflected in the line y = x. Work out the coordinates of the image of point D.

9.State whether the line segment joining A(−4, 3) and B(2, 6) is horizontal, vertical or neither, and give a reason for your answer.

10.A dog is tied by a lead 4 m long to a fixed ring on a straight garden wall. The wall extends much further than the lead can reach in both directions, and the dog cannot cross through it. Describe the region the dog can reach.

11.Write down which one of these statements about quadrilaterals is true.

12.A sector of a circle has radius 9 cm and angle 40°. Work out the area of the sector, in terms of π.

13.A trapezium-shaped allotment plot has two parallel sides that face each other, and two sloping sides that are equal in length (an isosceles trapezium). One of the angles next to the shorter parallel side is 118°. Work out the angle next to the other end of the same shorter parallel side.

14.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

15.A plan of a school hall uses a scale of 1 : 250. A wall is drawn 3.4 cm long on the plan. Sam wants to know the wall's real length in metres. What is it?