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Question
Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m
Solution
Here a = 1.8 m, b = 8 m, c = 8.2 m
s = `("a" + "b" + "c")/2`
= `((1.8 + 8 + 8.2)"m")/2`
= `18/2`
= 9 m
s – a = 9 – 1.8 = 7.2 m
s – b = 9 – 8 = 1 m
s – c = 9 – 8.2 m = 0.8
Area of triangle
= `sqrt("s"("s" - "a")("s" - "b")("s" - "c"))`
= `sqrt(9 xx 7.2 xx 1 xx 0.8)`
= `sqrt(9 xx 5.76)`
= `sqrt9 xx sqrt(576/100)`
= `3 xx 24/10`
= 3 × 2.4
= 7.2 m2
∴ Area of the triangle = 7.2 sq.m
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