1.

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

Answer»

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}}


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