For a triangle with side lengths $a, b, c$:
Step 1: Compute the Semi-Perimeter ($s$): $$\mathbf{s = \frac{a + b + c}{2}}$$
Step 2: Apply Heron's Formula: $$\mathbf{\text{Area} = \sqrt{s(s - a)(s - b)(s - c)}}$$
Problem: Find the area of a triangular plot whose sides are $13\text{ m}, 14\text{ m},$ and $15\text{ m}$.
Step 1: $s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21\text{ m}$.
Step 2: $s - a = 21 - 13 = 8\text{ m}$; $s - b = 21 - 14 = 7\text{ m}$; $s - c = 21 - 15 = 6\text{ m}$.
Step 3: $\text{Area} = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{(3 \times 7) \times (2 \times 4) \times 7 \times (2 \times 3)}$.
Pairing factors: $\sqrt{3^2 \times 7^2 \times 4^2} = 3 \times 7 \times 4 = 84\text{ m}^2$.