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2. 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
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3. Find the area of this triangle:
6 cm
30°
8 cm
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5. 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
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7. 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.]
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9. 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
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10. 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 ≈ 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
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11. © T Madas