Question

find the area of the triangle 20cm,22cm,24cm using Herons Fourmula.

Answer 1

To find : area of  triangle .

Given : sides of triangle are $20cm , 22cm , 24cm$

Solution :

• Let , a, b , c be the sides of triangle .

• We find area of triangle by Heron's Formula :

       $\text { Area of triangle }=\sqrt{s(s-a)(s-b)(s-c)}$

• Where, s = semi perimeter and ,a, b, c are sides of triangle.

        $s = \frac{20 + 22 + 24}{2} \\s = \frac{66}{2} \\s = 33$

• Putting values , we get

       $\begin{aligned}\text { Area } &=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{33(33-20)(33-22)(33-24)} \\&=\sqrt{33\times 13 \times 11 \times 9} \\&=\sqrt{11\times 3\times 13 \times 11 \times 3 \times 3 } \\&=3\times 11\sqrt{3 \times 13} \\&=33 \times\sqrt{3} \times \sqrt{13} \\&=33 \times \sqrt{39} \\&=33 \times 6.24\end{aligned}$

•  Area =   $205.92 \ cm^{2}$

Hence , area of given  triangle is $205.92 \ cm^{2}$ .