in a rectangular field of dimensions 50mx30m, a traingular park is constructed.if the sides of the park are 15m, 14m, and 13m, find the area of the remaining field( herons formula)
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Area of rectangle = 1500m^2
Given sides of triangular park = 15m , 14m , 13m
Area of triangle = √[ s(s-a)(s-b)(s-c) ] {Heron's formulae}
s = 15 + 14 + 13 /2 = 21m
where s is a + b + c/2 and a,b,c are sides
=> Area of triangle = √[ 21(21-15)(21-14)(21-13)]
= √[ 21(6)(7)(8)] = √[7056] = 84m^2
∴ Area of remaining field = Area of rectangle - Area of triangle = 1500 - 84 = 1416m^2
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