The shape of a plot is a rhombus. Its perimet | vedclass

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(B) Let $ABCD$ be the plot which is divided by the diagonal $BD = 72 \, m$ into two equal triangles.Since $ABCD$ is a rhombus,all its sides are equal.

Vedclass · Accepted Answer

$5544$

Vedclass · Answer

(B) Let $ABCD$ be the plot which is divided by the diagonal $BD = 72 \, m$ into two equal triangles.Since $ABCD$ is a rhombus,all its sides are equal.Perimeter $= 4 	imes 	ext{side} = 340 \, m$.Therefore,side $= \frac{340}{4} = 85 \, m$.In $\Delta ABD$,the sides are $a = 85 \, m$,$b = 85 \, m$,and $c = 72 \, m$.Semi-perimeter $(s) = \frac{85 + 85 + 72}{2} = \frac{242}{2} = 121 \, m$.Using Heron's formula,Area of $\Delta ABD = \sqrt{s(s-a)(s-b)(s-c)}$$= \sqrt{121(121-85)(121-85)(121-72)}$$= \sqrt{121 	imes 36 	imes 36 	imes 49}$$= 11 	imes 36 	imes 7 = 2772 \, m^2$.Since the diagonal divides the rhombus into two equal triangles,the total area of the rhombus $ABCD = 2 	imes 	ext{Area of } \Delta ABD$$= 2 	imes 2772 = 5544 \, m^2$.

The shape of a plot is a rhombus. Its perimeter is $340 \, m$ and one diagonal is $72 \, m$. Find its area. (in $, m^2$)

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