Geometry and measures worksheet — GCSE Foundation

1.A solid has two parallel, congruent polygon faces joined by flat rectangles, and its cross-section is the same shape all the way along its length. Which solid is it?

2.Triangle PQR has vertices P(0, 0), Q(9, 0) and R(0, 4). Work out the area of triangle PQR.

3.A solid has 5 faces: one square face and four triangular faces, which all meet at a single point above the square. What is the name of this solid?

4.Write down how many right angles a rectangle has.

5.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.

6.A sector of a circle has an angle of 90° at the centre. Write down what fraction of the whole circle this sector represents.

7.Two triangular offcuts of wood, PQR and STU, are cut for a construction project. PQ = 8 cm, QR = 6 cm and angle PQR = 90°. ST = 8 cm, TU = 6 cm and angle STU = 90°. A carpenter wants to check the two pieces are identical in shape and size before using them as a matching pair. Using only the measurements given, and without working out any further lengths, which condition proves that triangle PQR is congruent to triangle STU?

8.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.

10.Two triangles are congruent to each other. What does this tell you about their angles and sides?

11.A tangent to a circle with centre O touches the circle at point P, where OP = 5 cm. Point Q lies on the tangent so that PQ = 12 cm. Using the fact that a tangent is perpendicular to the radius at the point of contact, work out the length OQ.

12.A rhombus has all four sides equal in length. Which statement about a rhombus is correct?

13.P is the point (3, 4) and Q is the point (6, 0). Work out the distance of each point from the origin, and write down which point is closer to the origin.

14.Two angles lie on a straight line. One angle is 118°. Which reason correctly explains why the other angle is 62°?

15.A chord divides a circle into two regions, one larger than the other. Write down the term used for the smaller of these two regions.