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Area of a triangle: ½ab sin C worksheet — GCSE Higher

Fifteen questions on "area of a triangle: ½ab sin c" — DfE statement G23. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.

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Area of a triangle: ½ab sin C worksheet — GCSE Higher

Maths · GCSE Higher · G23 · Area of a triangle: ½ab sin C · 15 questions

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1.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
2.A regular hexagon has sides of length 8 cm. By splitting the hexagon into 6 identical triangles that meet at its centre, work out the area of the hexagon. Give your answer to 1 decimal place.
(a)192.0 cm²
(b)166.3 cm²
(c)138.6 cm²
(d)27.7 cm²
3.In triangle ABC, AB = 15.6 cm, AC = 8.9 cm and angle BAC = 112°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)128.7 cm²
(b)26.0 cm²
(c)64.4 cm²
(d)112.8 cm²
4.In triangle ABC, AB = 11 cm, AC = 9 cm and the area of the triangle is 45 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.
(a)65.4°
(b)27.0°
(c)153.0°
(d)114.6°
5.In triangle ABC, AB = 6 cm, AC = 8 cm and angle BAC = 60°. Work out the exact area of triangle ABC, giving your answer in the form $a 3$ .
(a) $93$ cm²
(b) $243$ cm²
(c) $123$ cm²
(d) $163$ cm²
6.ABCD is a convex quadrilateral field with diagonal AC = 20 m. In triangle ABC, AB = 14 m and angle BAC = 35°. In triangle ACD, AD = 16 m and angle DAC = 40°. Work out the total area of the field. Give your answer to 1 decimal place.
(a)108.2 m²
(b)80.3 m²
(c)91.6 m²
(d)183.1 m²
7.A rhombus-shaped floor tile has sides of length 12 cm and an interior angle of 55°. Work out the area of the tile. Give your answer to 1 decimal place.
(a)59.0 cm²
(b)82.6 cm²
(c)144.0 cm²
(d)118.0 cm²
8.In triangle ABC, AB = AC = 9 cm and angle ABC = angle ACB = 65°. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)26.0 cm²
(b)31.0 cm²
(c)62.0 cm²
(d)36.7 cm²
9.Which of these statements about the area formula Area = 1/2ab sin C is correct?
(a)AB, BC and angle ABC: Area = 1/2 × AB × BC × sin(BAC)
(b)Three sides, no angle: Area still = 1/2 AB×AC×sin(BAC)
(c)AB, AC and angle BAC: Area = 1/2 × AB × AC × sin(BAC)
(d)AB, AC and angle ABC: Area = 1/2 × AB × AC × sin(ABC)
10.A triangular solar panel has two edges of length 1.8 m and 1.3 m, with an angle of 72° between them. Manufacturing the panel costs £85 per square metre. Work out the total manufacturing cost. Give your answer to the nearest penny.
(a)£94.58
(b)£189.17
(c)£30.73
(d)£93.50
11.A parallelogram-shaped tile has two sides of 6 cm and 9 cm, with an angle of 60° between them. Work out the area of the tile. Give your answer to 1 decimal place.
(a)27.0 cm²
(b)46.8 cm²
(c)13.0 cm²
(d)23.4 cm²
12.A kite ABCD is symmetrical about the diagonal AC, with AB = AD = 6 cm and CB = CD = 9 cm. Angle ABC = 100°. By splitting the kite into two congruent triangles along AC, work out the area of the whole kite. Give your answer to 1 decimal place.
(a)106.4 cm²
(b)26.6 cm²
(c)54.0 cm²
(d)53.2 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 triangular sail for a small boat has two sides of 4.2 m and 3.6 m, with an angle of 115° between them. One litre of waterproofing paint covers 3 m² of sail. Work out the least number of whole tins of paint (1 litre each) needed to cover the sail.
(a)3
(b)2
(c)5
(d)7
15.In triangle ABC, AB = 12 cm, AC = 7 cm and the area of the triangle is 33 cm². Given that angle BAC is obtuse, work out the size of angle BAC. Give your answer to 1 decimal place.
(a)156.9°
(b)128.2°
(c)51.8°
(d)38.2°

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