Area of Triangle Using Heron's Formula

In triangle ABC, the lengths of the sides are given as follows: AB = 7, AC = 9, and BC = 10. Determine the area of triangle ABC using Heron's formula. Heron's formula states that the area S of a triangle with sides of lengths a, b, and c is given by:

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

where $s$ is the semi-perimeter defined as:

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