Calculating the Area of Triangle with Heron's Formula

Consider triangle ABC, where the lengths of sides AB, AC, and BC are given as follows:

• AB = 13
• AC = 14
• BC = 15

Determine the area of triangle ABC using Heron's formula, which states that the area $A$ of a triangle with sides of lengths $a$, $b$, and $c$ is given by:

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

where $s$ is the semi-perimeter, calculated as $s = \frac{a + b + c}{2}$. For this triangle, what is the area?