Geometry and measures worksheet — GCSE Foundation

1.The three angles of a triangle are 10°, 58° and 112°. Write down the name that describes this triangle.

2.A triangle has vertices A(0, 0), B(10, 0) and C(5, 12). Work out the area of the triangle.

3.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?

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

5.A cake recipe takes 135 minutes from start to finish. Write this time as hours and minutes.

6.A student draws a net using 5 identical squares arranged in a row of four with one extra square attached to the side of one of them. Can this net be folded to make a closed cube?

7.A ladder of length 7 m leans against a vertical wall. The foot of the ladder is 3 m from the base of the wall. Work out how high up the wall the ladder reaches. Give your answer correct to 1 decimal place.

8.The point (5, −2) is reflected in the x-axis. Work out the coordinates of the image point.

9.A solid has 6 faces: one pentagon and five triangles that all meet at a single point above the pentagon. What is the name of this solid?

10.Triangle ABC has a right angle at B and hypotenuse AC = 17 cm, with AB = 8 cm. Triangle DEF has a right angle at E and hypotenuse DF = 17 cm. Which extra fact about DEF would complete the RHS condition for proving that ABC ≅ DEF, with the vertices matching in that order?

11.Triangle ABC is similar to triangle PQR. Side AB is 8 cm and corresponds to side PQ, which is 12 cm. Side AC is 6 cm and corresponds to side PR. Work out the length of PR.

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

13.A cylinder has a radius of 3 cm and a height of 10 cm. Using π = 3.14, work out the volume of the cylinder.

14.A bearing is described as being exactly halfway between north and east, measured clockwise. What is the three-figure bearing?

15.A circle has centre O. PQ, RS and TU are three chords of the circle, and only one of them passes through O. Write down what this tells you about that chord.