Question

The area of a triangle by Heron's formula is

• A. $\sqrt{(s-a)(s-b)(s-c)}$
• B. $\sqrt{s(s-a)(s-b)(s-c)}$
• C. $\sqrt{(s+a)(s-b)(s-c)}$
• D. $\sqrt{(s+a)(s+c)(s+c)}$

Answer 1

The correct option is B $\sqrt{s(s-a)(s-b)(s-c)}$

Using Herons formula, we first have to find the semi perimeter with sides $a,b$ and $c$:

$s=\frac{a+b+c}{2}$

And then area of the triangle is:

$A=\sqrt{s(s-a)(s-b)(s-c)}$

Hence, area of a triangle by heron's formula is $A=\sqrt{s(s-a)(s-b)(s-c)}$.