Question

By herons formulae find out the area of a equilateral triangle whose side is 16 cm.

Answer 1

Answer :

We know Heron's formula :

Area of triangle = $\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

Here

a , b and c are sides of triangle , So a = b = c = 16 cm ( Given we have equilateral triangle )

And

s = $\frac{a+b\hspace{0.17em}+c}{2}$ , So

s = $\frac{16+16\hspace{0.17em}+16}{2}=\frac{48}{2}$ = 24

So,

Area of given equilateral triangle = $\sqrt{24\left(24-16\right)\left(24-16\right)\left(24-16\right)}=\sqrt{24\times 8\times 8\times 8}=\sqrt{12288}=\mathbf{110}\mathbf{.}\mathbf{85}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathbf{Ans}\mathbf{}\mathbf{)}$