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© T Madas

There is a trigonometric formula for the area of a triangle. This is how it is derived: Opp Hyp sinθ = c h a a sinθ = c h h = a x sinθ θ b © T Madas

Find the area of this triangle: 6 cm 30° 8 cm © T Madas

© T Madas

Calculate the area of a regular hexagon of side 8 cm, giving your answer to 3 significant figures. x sin60° c AT = 32 sin60° c O AH = c F C 192 sin60° AH = 166 cm2 [ 3 s.f.] 60° 8 cm 60° 60° A B 8 cm © T Madas

© T Madas

A regular decagon is inscribed in a circle of radius 4 cm. Calculate the area of the octagon, giving your answer correct to 3 significant figures. The area of the triangle OAB 1 2 A = x 4 x 4 x sin36° c A A ≈ 4.702 cm2 4 cm O 36° The area of the decagon B 10 x 4.702 = 47.0 cm2 [ 3 s.f.] © T Madas

© T Madas

The area of the triangle ABC The triangle ABC has AB = 30 m, RABC = 30° and has an area of 300 m2. Calculate the perimeter of the triangle, giving your answer correct to 3 significant figures. The area of the triangle ABC B 1 2 A = x 30 x x x sin30° c 30° 1 2 x 300 = x 30 x x x sin30° c 40 m 30 m 1 2 1 2 4 x 300 = x 30 x x x x 4 c 300 m2 A C 1200 = 30x c y x = 40 © T Madas

By the cosine rule on ABC The triangle ABC has AB = 30 m, RABC = 30° and has an area of 300 m2. Calculate the perimeter of the triangle, giving your answer correct to 3 significant figures. B By the cosine rule on ABC y 2 = 302 + 402 – 2 x 30 x 40 x cos30° c 30° y 2 = 900 + 1600 – 2400 cos30° c 40 m 30 m y 2 ≈ 421.539 c 300 m2 y ≈ 20.53 m A C 20.53 m y Therefore the perimeter of VABC to 3 s.f. is 90.5 m © T Madas

© T Madas