Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Higher

Maths · GCSE Higher · Geometry and measures · Calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A parallelogram has an area of 84 cm² and a base of 12 cm. Work out the perpendicular height of the parallelogram.
(a)0.14 cm
(b)1008 cm
(c)3.5 cm
(d)7 cm
2.A right-angled triangle has a hypotenuse of 8 cm, and one of its shorter sides is 4 cm. Work out the size of the angle between that 4 cm side and the hypotenuse.
(a)90°
(b)45°
(c)30°
(d)60°
3.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.
(a)4.0 m
(b)6.4 m
(c)6.3 m
(d)10.0 m
4.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.
(a)75°
(b)105°
(c)37°
(d)146°
5.A sprinkler waters a sector-shaped patch of a garden with radius 8 m and angle 90°. Work out the perimeter of the watered sector, to 1 decimal place. (Use π = 3.14.)
(a)28.6 m
(b)20.6 m
(c)12.6 m
(d)41.1 m
6.A regular octagonal tabletop has centre O. Each vertex is 30 cm from O. Work out the area of the tabletop. Give your answer to the nearest square centimetre.
(a)1909 cm²
(b)5091 cm²
(c)318 cm²
(d)2546 cm²
7.A photograph is 10 cm wide and 15 cm tall. It is enlarged to make a similar poster that is 40 cm wide. The poster costs £0.80 per centimetre of its height to print, based on its full height. Work out the cost of printing the poster.
(a)£3
(b)£15.20
(c)£12
(d)£48
8.In triangle ABC, AB = 8.6 cm, AC = 11.4 cm and angle BAC = 47°. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)35.9 cm²
(b)71.7 cm²
(c)33.4 cm²
(d)52.6 cm²
9.A rectangle has vertices A(0, 0), B(6, 0), C(6, 4) and D(0, 4). Work out the length of the diagonal AC. Give your answer correct to 2 decimal places.
(a)26.00 units
(b)4.47 units
(c)10.00 units
(d)7.21 units
10.A sector of a circle has radius 9 cm and angle 120°. Using π = 3.14, work out the arc length of the sector, to 1 decimal place.
(a)56.5 cm
(b)37.7 cm
(c)9.4 cm
(d)18.8 cm
11.Two similar company logos are printed at different sizes. The area of the larger logo is 2.25 times the area of the smaller logo. Work out the length scale factor from the smaller logo to the larger logo.
(a)2.25
(b)5.0625
(c)1.5
(d)1.125
12.A solid ball has a radius of 7 cm. Work out the surface area of the ball. Use π = 3.14.
(a)615.44 cm²
(b)1436.03 cm³
(c)153.86 cm²
(d)87.92 cm²
13.A garden is made of two triangular flower beds, ABC and ACD, joined along the edge AC. In triangle ABC, angle ABC = 90°, AB = 5 m and BC = 12 m. In triangle ACD, AD = 9 m and angle CAD = 40°, the angle between AC and AD. Work out the area of flower bed ACD. Give your answer to 1 decimal place.
(a)49.2 m²
(b)44.8 m²
(c)37.6 m²
(d)14.5 m²
14.A sector of a circle has radius 12 cm and angle 45°. Using π = 3.14, work out the area of the sector.
(a)9.42 cm²
(b)452.16 cm²
(c)56.52 cm²
(d)4.71 cm²
15.A map has a scale of 1 : 20 000. The distance between two villages is 3.4 km in real life. How long is this distance on the map, in centimetres?
(a)17 cm
(b)0.17 cm
(c)1700 cm
(d)170 cm

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