Question

find the area of a triangular lot with side length 50 meters, 65 meters, and 81 meters (complete solution).

Answer 1

Given :

• Sides of the triangular plot = 50 m, 65 m and 81 m.

To find :

• Area of the triangular plot = ?

Step-by-step explanation :

Now, the formula to find the semi-perimeter of a triangle is :-

$\bigstar {\boxed {\bf S = \dfrac{ a+ b+ c}{2}}}$

Substituting value in above formula, we get

$\begin{lgathered} \tt S = \dfrac{ 50 + 65 + 81 }{2}\\ \\ \tt =\dfrac{196}{2}\\ \\ \tt= 196 \div 2\\ \\ \tt= 98 \: m\end{lgathered}$

Now, by Heron's formula find the area of the triangular plot :

$\bigstar{\boxed{\bf Area \:of \triangle = {\sqrt{s(s-a) (s-b) (s-c)}}}}$

Substituting value in the above formula, we get,

${\tt = {\sqrt{98(98-50) (98-65) (98-81)}}} \\ \\ \tt = {\sqrt{98\times 48 \times 33 \times 17}} \\ \\ \tt = {\sqrt{2\times7\times7\times2\times2\times2\times2\times3\times3\times11\times17}} \\ \\ \tt = 2 \times 7 \times 2 \times 3{\sqrt{11\times17\times2}} \\ \\ \tt = 84{\sqrt{374}}$

Thus, The Area of the triangular plot$\tt = 84{\sqrt{374\:m^2}}$

Answer 2

$\huge {\red{\mathfrak {Question :-}}}$

• Find the area of a triangular plot with side length 50 meters, 65 meters, and 81 meters.

$\huge {\pink{\mathfrak {Solution :-}}}$

$\underline{\bold {Given:}}$

• Sides of the triangular plot = 50 meters , 65 meters and 81 meters.

$\underline{\bold {To find :}}$

• The area of the triangular plot.

We have to find area so we first find semi-perimeter :

$\boxed {\blue{S = \dfrac{ a+ b+ c}{2}}}$

Let

• a=50 meters
• b=65 meters
• c=81 meters.

$\begin{lgathered}\begin{lgathered} \implies S = (\dfrac{ 50 + 65 + 81 }{2})\:meters\\ \\ \implies S=(\dfrac{196}{2}) \: meters\\ \\ \implies S= 98 \: meters \end{lgathered}\end{lgathered}$

By Heron's formula we find the area of the triangular plot :

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

$\begin{lgathered}{={\sqrt{98(98-50) (98-65) (98-81)}}} \: meters \\ \\ = {\sqrt{98\times 48 \times 33 \times 17}} \: meters\\ \\={\sqrt{2\times7\times7\times2\times2\times2\times2\times3\times3\times11\times17}} \: meters\\ \\ =2 \times 2\times 7\times 3{\sqrt{2\times11\times 17}} \: meters \\ \\ = 84{\sqrt{374}} \: meters\end{lgathered}$

$\green {\therefore {The\:area\: of \:the\:triangular\: plot\:is\:84{\sqrt{374}\:meters.}}}$

$\rule {307}{2}$