Geometry and measures worksheet — GCSE Foundation

1.A line segment is measured with a ruler and found to be 6.5 cm long. What is this length in millimetres?

2.Two sides of a triangle are 20 cm and 8 cm long. Write down which one of these lengths is possible for the third side.

3.The bearing of a harbour B from a ferry's position A is 260°. What is the bearing of A from B?

4.Work out the distance between the point (0, 0) and the point (5, 12).

5.a is the column vector with top number 3 and bottom number −2. Work out 4a, giving your answer as a column vector in the form (top, bottom).

6.A roof truss is shaped like an isosceles triangle resting on a horizontal ceiling joist. The truss's sloping edges are equal in length, and the angle at its apex is 40°. The ceiling joist continues in a straight line beyond the foot of the truss. Work out the angle between the truss's sloping edge and the extended joist, on the outside of the truss.

7.How many vertices does a square-based pyramid have?

8.Write down the column vector, from the options given, that would move a point to the right and downwards.

9.Compasses are opened to exactly half the length of AB, and arcs are drawn centred at A and at B, to construct the perpendicular bisector of AB. Why does this fail?

10.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.

11.A scale model of a bridge is built so that 2 cm on the model represents 5 m of the real bridge. The real bridge is 45 m long. Work out the length of the model bridge, in centimetres.

12.The point (4, −3) is reflected in the y-axis. Work out the coordinates of the image point.

13.The point A(3, 2) is translated by the vector (−5, 4) to give point B. Work out the coordinates of B.

14.A straight fence is 5 m long. Describe the shape of the region made up of every point on the ground within 2 m of any part of the fence.

15.Write down the term for the distance all the way around the edge of a circle.