Question

in a rectangular field of dimensions 125 m multiply 80 m a triangular park is constructed .if the dimension of the park are 50m 78m and one 112m .find the area of the reamension field

Answer 1

$area \: of \: square \\ = 125 \times 80 \\ 10 \: 000 \: {m}^{2} \\ \\ \\ \\ area \: of \: triangle \\ s= \frac{a + b + c}{2} \\ \\ s = \frac{78 + 50 + 112}{2} \\ \\ s = \frac{240}{2} \\ \\ s = 120 \\ \\ (s - a) = (120 - 112) = 8\\ (s - b) = (120 -78 ) = 42\\ (s - c) = (120 - 50) = 70 \\ \\ using \: heron \: formula \\ \\ = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ = \sqrt{120(8)(42)(70)} \\ \\ \\ = 1682 \: {m}^{2} \\ area \: of \: remaining \: portion \: \\ = area \: of \: rectange - area \: of \: triangle \\ \\ = 10000 - 1682 \\ \\ = 8320 \: {m}^{2}$

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