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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.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
2.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
3.In triangle ABC, AB = 9.4 cm, AC = 7.2 cm and angle BAC = 63°, the angle between them. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)60.3 cm²
(b)15.4 cm²
(c)39.4 cm²
(d)30.2 cm²
4.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
5.In triangle ABC, AB = 15 cm, angle BAC = 38° and the area of the triangle is 61 cm². Work out the length of BC. Give your answer to 1 decimal place.
(a)13.2 cm
(b)9.3 cm
(c)10.6 cm
(d)26.7 cm
6.The area of triangle ABC is 42 cm². AB = 9.5 cm and angle BAC = 61°. Work out the length of AC. Give your answer to 1 decimal place.
(a)10.1 cm
(b)7.7 cm
(c)18.2 cm
(d)5.1 cm
7.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)
8.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
9.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
10.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
11.In triangle ABC, angle ABC = 58°, angle ACB = 47° and BC = 14 cm. Work out the area of triangle ABC. Give your answer to 1 decimal place.
(a)83.1 cm²
(b)81.6 cm²
(c)62.9 cm²
(d)71.7 cm²
12.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.
(a)63.0 m²
(b)40.5 m²
(c)49.5 m²
(d)60.5 m²
13.A circle has centre O and radius 10 cm. Points A and B lie on the circle such that angle AOB = 130°. Work out the area of the minor segment cut off by the chord AB. Give your answer to 1 decimal place.
(a)113.4 cm²
(b)75.1 cm²
(c)38.3 cm²
(d)162.4 cm²
14.Triangle 1 has sides of 10 cm and 13 cm with an angle of 64° between them. Triangle 2 has sides of 11 cm and 12 cm with an angle of 70° between them. Which triangle has the greater area, and by how much? Give your answer to 1 decimal place.
(a)Triangle 2, by 33.5 cm²
(b)Triangle 1, by 54.8 cm²
(c)Triangle 1, by 3.6 cm²
(d)Triangle 2, by 3.6 cm²
15.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

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