Heron's Formula

Problem Description

Given the lengths of the three sides of a triangle, compute its area.

Input Format

The input is three real numbers: the lengths of the three sides.

Output Format

Output the area of the triangle, kept to 2 decimal places.

Sample Input

3 4 5

Sample Output

6.00

Hint

• The sides may be decimals — pick the right type.
• Apply the formula: first compute $p$, then compute $S$. sqrt is in <cmath>. Keep 2 decimal places.
• Check against the sample: 3 4 5 → 6.00.

Heron's formula: let the three sides of the triangle be $\,a,b,c$, set $\,p=\frac{a+b+c}{2}$, then the area of the triangle $\,S=\sqrt{p(p-a)(p-b)(p-c)}$.