Geometry and measures worksheet — GCSE Higher

1.In triangle ABC, angle ABC = 47°, AC = 12.5 cm and BC = 9.2 cm. Work out the size of angle BAC. Give your answer to 1 decimal place.

2.In geometry, which of the following best describes a 'plane'?

3.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.

5.In triangle ABC, AB = 7.4 cm, AC = 5.9 cm and angle BAC = 68°. Work out the length of BC. Give your answer to 1 decimal place.

6.A parallelogram has an area of 96 cm² and a base of 8 cm. Work out the perpendicular height of the parallelogram.

7.e is the column vector with top number 5 and bottom number k. f is the column vector with top number 15 and bottom number 6. Given that f is 3 times e, work out the value of k.

8.A patio plan states: 'Side AB of the patio is parallel to side DC, and AB is longer than DC. Sides BC and AD are not parallel to each other and are not equal in length.' The four sides measure AB = 5.1 m, BC = 3.2 m, DC = 2.8 m and AD = 4.5 m. The tiler needs to order edging strip only for the sides that are not parallel to any other side. What total length of edging strip, in metres, should the tiler order?

9.Which of these correctly compares a 'line' with a 'line segment'?

10.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.

11.A ramp is built from two straight metal supports that rest on the flat ground and meet each other at the top, forming a triangle with the ground. One support meets the ground at 34°. The angle between the two supports where they meet is 71°. Work out the angle between the second support and the ground.

12.Triangle ABC has AB = 6 cm and BC = 9 cm, with angle A = 40°. Triangle DEF has DE = 6 cm and EF = 9 cm, with angle D = 40°. Meera says these facts prove the triangles are congruent by SAS. Is Meera correct?

13.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.

14.A sector of a circle has radius 6 cm and angle 150°. Using π = 3.14, work out the perimeter of the sector.

15.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.