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The Area of a Triangle

A. b. c. h. B. C. D. a. The Area of a Triangle. In triangle ABC to the right:. AD is perpendicular to BC. So the area of ABC is given by:. Area = ½  BC  AD………(1). Substituting (2) into (1). Area = ½  BC  AC  sin C. Area = ½  a  b  sin C. Area = ½absinC. 68 .

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The Area of a Triangle

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  1. A b c h B C D a The Area of a Triangle In triangle ABC to the right: AD is perpendicular to BC So the area of ABC is given by: Area = ½  BC  AD………(1) Substituting (2) into (1) Area = ½  BC  AC  sinC Area = ½  a  b  sinC Area = ½absinC

  2. 68 234m 413m 100m 100m Example 1 Find the area of this field in hectares. Area = ½absinC = ½  413  234  sin68 = 44802·45m2 = 4·48ha Remember 1 hectare = 10 000m2 10 000m2

  3. P 56 23·6m 43·6m Q R Example 2 Find the area of PQR, if P = 56°, q = 23·6m and r = 43·6m. Draw a diagram first. Label diagram. Area = ½qrsinP = ½  23·6  43·6  sin56 = 426·52m2

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