Geometry and measures worksheet — GCSE Higher

1.A written description of a diagram states: 'AB is marked with a single arrow, CD is marked with a single arrow, and EF is marked with a double arrow.' Using the standard convention for marking parallel lines, what can be concluded?

2.A picture frame is a rhombus with a diagonal of 16 cm and a diagonal of 12 cm. The two diagonals meet at right angles at their midpoints. Work out the length of one side of the rhombus.

3.A triangular flower bed ABC has AB = 14 m, BC = 9 m and AC = 11 m. Work out the area of the flower bed. Give your answer to 1 decimal place.

4.Triangle DEF has a right angle at E. Angle DFE = 60° and EF = 9 cm. Work out the exact length of DE.

5.In triangle ABC, AB = 6 cm, angle ABC = 40° and AC = 9 cm. Using the sine rule, sin(ACB) = AB × sin(ABC) ÷ AC, which gives two possible values for angle ACB: 25.4° or 154.6° (each to 1 decimal place). By considering the angle sum of the triangle, decide which of these two values angle ACB can actually take, and hence work out angle BAC. Give your answer to 1 decimal place.

6.A right-angled triangle has a hypotenuse of 10 cm and one of its other angles is 45°. Work out the length of one of the two shorter sides. Give your answer to 1 decimal place.

7.Shape S has an area of 48 cm². It is enlarged by a scale factor of 1/4 to give shape T. Work out the area of shape T.

8.Two similar triangles have lengths in the ratio 5 : 8. A side of the smaller triangle is 6.5 cm. Work out the length of the corresponding side of the larger triangle.

9.The diagram shows a solid made from two cuboids joined together. Which shape is the front elevation of this solid?

10.A circle has circumference 31.4 cm. Using π = 3.14, work out the radius of the circle.

11.In triangle ABC and triangle DEF, AB = DE, AC = DF, and the angle at A equals the angle at D. Write down the congruence condition that proves the two triangles are congruent.

12.In triangle OAB, OA = a and OB = b. P lies on AB such that AP is twice PB. Express the vector OP in terms of a and b.

13.A water tank holds 2.5 m³. Work out this volume in cm³.

14.A cuboid has length 3 cm, width 4 cm and height 12 cm. Work out the length of the diagonal that runs from one corner of the cuboid to the opposite corner.

15.From an external point P, two tangents PA and PB touch a circle with centre O at the points A and B. Angle APB = 50°. Work out the size of angle OAB.