Since all the sides of the triangle are known, it is better to use Heron's formula for finding the area.
Consider the sides of the triangle as,
[tex]\begin{gathered} a=10 \\ b=14 \\ c=15 \end{gathered}[/tex]
Solve for the semi-perimeter (s) as,
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{10+14+15}{2} \\ s=19.5 \end{gathered}[/tex]
Then according to the Heron's Formula, the area (A) of the triangle is given by,
[tex]A=\sqrt[]{s(s-a)(s-b)(s-c)}[/tex]
Substitute the values and simplify,
[tex]\begin{gathered} A=\sqrt[]{19.5(19.5-10)(19.5-14)(19.5-15)} \\ A=\sqrt[]{19.5\times9.5\times5.5\times4.5} \\ A=\sqrt[]{4584.9375} \\ A\approx67.7 \end{gathered}[/tex]
Thus, the area of the given triangle is 67.7 sq. km approximately.
