Question

Find the area of a triangle with legs that are: 16 m, 12 m, and 8 m.A. 38.2 m²B. 46.5 m²C. 54 m²D. 16.4 m²

Answer 1

To calculate the area of a triangle with 3 sides given, we use Heron's formula.

Heron's formula is given below;

$\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where s is the semi perimeter} \\ s=\frac{a+b+c}{2} \\ \text{where } \\ a=8m \\ b=12m \\ c=16m \\ \end{gathered}$

Thus,

$\begin{gathered} s=\frac{8+12+16}{2} \\ s=\frac{36}{2} \\ s=18m \end{gathered}$$\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{18(18-8)(18-12)(18-16)} \\ A=\sqrt[]{18\times10\times6\times2} \\ A=\sqrt[]{2160} \\ A=\pm46.4758m^2 \\ \text{Area cannot be negative, thus} \\ A=46.4758m^2 \\ A\approx46.5m^2 \end{gathered}$

Therefore, the area of the triangle with legs 16m, 12m, and 8m is 46.5 square meters

The correct answer is option B.