Question

use heron's formula to find the area of the triangle a=6in b=13 in c= 8in

Answer 1

Heron's formula is:

$\begin{gathered} \text{Area}=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \\ s=\frac{a+b+c}{2} \end{gathered}$

so, when a = 6 in , b = 13 in and c = 8 in

$s=\frac{6+13+8}{2}=\frac{27}{2}=13.5in$

And the area will be:

$\begin{gathered} A=\sqrt[]{13.5(13.5-6)(13.5-13)(13.5-8)}=\sqrt[]{13.5\cdot7.5\cdot0.5\cdot5.5} \\ \\ A=\sqrt[]{278.4375}=16.686in^2 \end{gathered}$

So, the answer will be the area of the triangle = 16.686 square inches