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Calculating the Area of a Triangle with Varying Parameters

This guide explains how to calculate the area of a triangle using various parameters such as base, height, and angles. Key formulas include the area calculated from height and base (Area = 1/2 * base * height) and using sine functions in cases where two sides and an included angle are known (Area = 1/2 * a * b * sin(C)). Example calculations are provided, demonstrating how to apply these formulas effectively, including scenarios with specific measurements. Suitable for students and enthusiasts of geometry.

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Calculating the Area of a Triangle with Varying Parameters

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  1. A C B a 1 = A ah 2 Area of Triangle c b h

  2. A c = h c sin B 1 = Area ah 2 C B a 1 = ac sin B 2 • If only a, c and  ABC are given …. h

  3. A b c a B N C Other case h

  4. A 1 = Area ab sin C c b 2 1 = bc sin A 2 B C a 1 = ca sin B 2 In conclusion

  5. A 9 cm 8 cm 120° C B 1 2 = x x x  Area ( 8 9 sin120 )cm 2 2 = 31.2cm Example 1

  6. Y = Area 32 cm 2 10 cm X Z 8 cm Example 2 :

  7. = Area 110 cm 2 P = Area 110cm 2 18 cm x cm = 17 . 3 R Q Example 3 :

  8. A B 4 cm 130° 1 = x x x ° Area of BCD ( 4 5 sin130 )cm 2 5 cm C D 2 = 7.660 4cm 2 = x 2 area of BCD = x (2 7.660 4) cm 2 = 15.3cm 2 Example 4 :

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