Geometry and measures worksheet — GCSE Foundation

1.A cuboid has three different edge lengths: a length, a width and a height, all different from each other. How many rectangles make up its net in total?

2.A quadrilateral has exactly two lines of symmetry, its two pairs of opposite angles are equal, and its diagonals are not equal in length. Write down the name of this quadrilateral.

3.A cuboid has a length, width and height that are all different from each other. How many planes of symmetry does it have?

4.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?

5.A map has a scale of 1 : 25000. A distance between two points measures 2 cm on the map. What is the real distance, in kilometres?

6.The diagram shows the plan, front elevation and side elevation of a solid. Which solid could this be?

7.Work out the exact value of sin 45° × cos 45°.

8.p is the column vector with top number 5 and bottom number 2. q is the column vector with top number 1 and bottom number 6. Work out p + q, giving your answer as a column vector in the form (top, bottom).

9.A regular polygon has 5 lines of symmetry. What is the order of rotational symmetry of this polygon?

11.Write down the name given to a quadrilateral that has exactly one pair of parallel sides.

12.A right-angled triangle has a hypotenuse of 14 cm. One of the other angles is 30°. Work out the exact length of the side opposite the 30° angle.

14.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

15.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?