Logarithm-5

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Find the area of the triangle whose sides are 47.69 cm, 32.92 cm and 57.01 cm

Solution: The area of the triangle, A = √(s(s - a)(s - b)(s - c))

where s = (a + b + c) / 2 = (47.69 + 57.01 + 32.92) / 2 = 68.81

s - a = 68.81 - 47.69 = 21.12

s - b = 68.81 - 57.01 = 11.8

s - c = 68.81 - 32.92 = 35.89

Therefore, A = √(68.81 (21.12) (11.8) (35.89))

Taking logarithm on both sides

log A = 1/2 [ log 68.81 + log 21.12 + log 11.8 + log 35.89 ]

= 1/2 [ 1.8377 + 1.3247 + 1.0719 + 1.555]

= 1/2 X 5.7893 = 2.8947

antilog 2.8947 = 784.7

Area of the triangle = 784.7 cm2

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