A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4…

A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as $4 \mathrm{~cm} .5 \mathrm{~cm}$ and $7 \mathrm{~cm}$. Then the area of land of the farmer in sq. $\mathrm{cm}$ is
  1. $2 \sqrt{6}$
  2. $4 \sqrt{6}$
  3. $\sqrt{6}$
  4. $8 \sqrt{6}$

Solution

$a=4 \mathrm{~cm}, b=5 \mathrm{~cm}, c=7 \mathrm{~cm}$ $\begin{aligned} & s=\frac{a+b+c}{2}=\frac{4+5+7}{2}=8 \mathrm{~cm} \\ & \text { Area of triangle }=\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{8 \times 4 \times 3 \times 1} \\ & =4 \sqrt{6} \mathrm{~cm}^2\end{aligned}$

Asked in: AP EAMCET 2022 (05 Jul Shift 2)

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