Geometry and measures worksheet — GCSE Foundation

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

2.A is the point (1, 3) and B is the point (7, 3). Work out the coordinates of the midpoint of AB.

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

4.In this question, a curved surface counts as a face. How many faces does a sphere have?

5.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

6.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?

7.A carpenter measures two triangular braces. Brace 1 has a 55° angle, a 65° angle, and, opposite the 55° angle, a side of 8 cm. Brace 2 has matching 55° and 65° angles and, opposite its 55° angle, a side of 8 cm. The carpenter says that because the equal 8 cm side is not between the two equal angles in either brace, he cannot be sure the two braces are the same size. Is the carpenter correct?

8.The bearing of a campsite B from a walker's position A is 070°. What is the bearing of A from B?

9.The diagram shows a cuboid. Work out the area of its front elevation, in square centimetres.

10.An isosceles triangle ABC has AB equal to AC. AM is a line from vertex A, perpendicular to BC, meeting BC at point M. Which condition proves that triangle ABM is congruent to triangle ACM?

11.Triangle ABC has AB = 10 cm, BC = 7 cm and angle A = 40°. Triangle DEF has DE = 10 cm, EF = 7 cm and angle D = 40°. Sam says the two triangles are congruent by SAS. Which statement about Sam's claim is correct?

12.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.

13.A square tile has sides of length 4.5 cm. Work out the perimeter of the tile.

14.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

15.A shape is made by joining two rectangles edge to edge, with no overlap. One rectangle measures 12 cm by 4 cm and the other measures 4 cm by 8 cm. Work out the total area of the shape.