Geometry and measures worksheet — GCSE Foundation

1.A hiker starts by walking on a bearing of 245°. She turns clockwise through 50°, then turns clockwise through a further 15°, and continues walking in a straight line. What bearing is she now walking on?

2.A shop stacks identical storage crates in a display. The diagram shows the plan of the floor positions used, with one corner position marked. Every floor position is filled with crates stacked 3 high, except the marked corner position, which is left completely empty. Work out how many crates are used in total.

3.A train leaves Leeds at 08:47 and arrives in London at 11:05. Work out how long the journey takes.

4.A rectangle has vertices A(1, 1), B(4, 1), C(4, 5) and D(1, 5). Work out the perimeter of the rectangle.

5.A triangle has vertices A(1, 1), B(5, 1) and C(5, 4). Work out the lengths of AB, BC and CA, and write down whether triangle ABC is right-angled.

6.A water tank holds 2.5 m³. Work out this volume in cm³.

7.How many edges does a triangular prism have?

8.A chord is drawn across a circle, dividing the circle into two regions. Write down the name of one of these two regions.

9.A cable supporting a flagpole is anchored to the ground 5 m from the base of the pole. The cable makes an angle of 60° with the ground. Using the exact value of tan 60°, work out the exact height of the flagpole.

10.A tent is shaped like a triangular prism: two triangular end faces and three rectangular faces. One of the rectangular faces lies flat on the ground as the groundsheet. How many of the tent's faces are above the ground, not touching the ground?

11.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?

12.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

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

14.Triangle ABC is isosceles, with AB = AC. Angle B = 70°. Which reason correctly explains why angle C = 70°?

15.A circular coaster has a radius of 4 cm. Work out the circumference of the coaster. Give your answer in terms of π.