Geometry and measures worksheet — GCSE Foundation

1.A church tower is due east of a village. What is the three-figure bearing of the church tower from the village?

2.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

3.Point D is at (3, 4). It is rotated 90° clockwise about the origin (0, 0). Work out the coordinates of the image of point D.

4.Triangle DEF is isosceles, with DE = DF. Angle E = 58°. Work out angle F.

5.A garden shed is shaped like a triangular prism: two identical vertical triangular end walls (the gable ends), joined by a sloping rectangular roof and a vertical rectangular back wall. Looking at the shed from directly above (the plan view), what shape is seen?

6.Triangle PQR has angle P = 90°. The side PQ = 9 cm and the hypotenuse QR = 15 cm. Work out the length of PR.

7.How many edges does a cube have?

8.A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

9.A sailmaker cuts two triangular sail panels from a pattern. Panel X has a 10 m side, with angles of 50° and 75° at its two ends. Panel Y also has a 10 m side, with angles of 50° and 75° at its two ends, in the same arrangement. The sailmaker wants to check the panels will match exactly, without cutting a third measurement. Which condition proves the two panels are congruent?

10.In parallelogram ABCD the vertices are labelled in order round the shape, so angle A and angle B are at the two ends of the same side. Angle A is 70°. Work out the size of angle B.

11.A warehouse stores identical cube-shaped crates. Its plan view is a 2 by 4 rectangle of crate positions, and every position is filled to a height of 3 crates, except one corner position, which has only 2 crates stacked on it because a delivery was incomplete. How many crates are there in total?

12.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.

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

14.A rectangular tile measures 4.5 cm by 6 cm. Work out the area of the tile.

15.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?