Question

A parallogram has two side 60m and 25m and a digonal 65m long. Find the area of the parallogram

Answer 1

$\huge\mathbb{\underline{\underline{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{side\:of\: parallelogram=60m\:and\:25m}\\ \sf{one\: diagonal=65m}\end{cases}$

$\huge\bf{To\:Find}$

The area of parallelogram

$\sf\underline{\pink{According\:to\: Question:-}}$

$\sf\underline{\underline{\red{Area\:of\: parallelogram=Base\times height}}}$

• In parallelogram there is two triangle
• if we add the area of 2 triangle we get the area of parallelogram

Area of parallelogram is

$\sf 2\times Area \:of\: triangle$

• Now lets find the area of ∆

$\sf By\: heron's\: formula\\ \\ \sf\implies \sqrt{s(s-a)(s-b)(s-c)}$

$\bold{we\:have}\begin{cases}\sf{a=60m}\\ \sf{b=25m}\\ \sf{c=65m}\end{cases}$

$\tt s=semi\:peimeter\\ \\ \tt s=\frac{a+b+c}{2}\\ \\ \tt s=\frac{65+25+60}{2}=\frac{150}{2}\\ \\ \sf\implies semiperimeter=72m$

$\boxed{\sf{Now\:Area\:of \triangle}}$

$\sf Area_\triangle=\sqrt{75(75-65)(75-60)(75-25)}\\ \\ \sf\leadsto Area_\triangle=\sqrt{75\times 10\times 15\times 50}\\ \\ \sf\leadsto Area_\triangle=\sqrt{15\times 5\times 10\times 15\times 10\times 5}\\ \\ \sf\leadsto Area_\triangle=15\times 5\times 10\times 5\\ \\ \sf\leadsto Area_\triangle=750\times 5\\ \\ \sf\implies Area_\triangle=3750$

• The area of the triangle of parallelogram is
• $\sf\implies 3750m{}^{2}$

$\tt Area\:of\:parallelogram \\ \\ \sf\leadsto 2\times Area \:of\: triangle \\ \\ \tt\leadsto Area\:of_{parallelogram}=2\times 3750\\ \\ \tt\implies Area\:of_{paralleogram}=7500cm{}^{2}$

$\boxed{\mathfrak{\purple{Area\:of_{parallelogram}=7500cm{}^{2}}}}$

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