Geometry and measures worksheet — GCSE Foundation

1.Triangle PQR has vertices P(0, 0), Q(6, 0) and R(0, 8). Work out the perimeter of the triangle.

2.A fish tank is a cuboid measuring 40 cm long, 25 cm wide and 30 cm high. Water is poured in to a depth of 20 cm. Work out the volume of water in the tank, in litres.

3.A straight line passes through points A, B and C, with B between A and C. A fourth point D is not on the line. Angle ABD = 132°. Work out the size of angle DBC.

4.A rectangular bookmark measures 2 cm by 25 cm. Work out the area of the bookmark.

5.Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

6.Write down which one of these quadrilaterals always has diagonals that are equal in length and that cross at right angles.

7.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

8.Two points on a circle divide its circumference into two arcs of different lengths. Write down the name given to the shorter of the two arcs.

9.In triangle ABC the angle at A is 90° and BC = 10 cm. For the angle at B, sin B = 3/5. Work out the length of AC.

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

11.A surveyor is marking out field ABCD for a new crop. The plan states that side AB is parallel to side DC, but AB and DC are not equal in length, and sides BC and AD are not parallel to each other. Which term correctly describes the shape of field ABCD?

12.Vertex X of a triangle is at (−3, 5). After a translation, the image of X is at (2, −1). Write down the column vector of this translation.

13.In the RHS congruence condition, which three facts must be true about two triangles for RHS to prove they are congruent?

14.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.

15.The point (2, 5) is translated 3 units right and 4 units down. Work out the coordinates of the image point.