Calculate the semi-perimeter

Calculate the semi-perimeter $s$ using the formula $s = \frac{a+b+c}{2}$.

$s = \frac{13+14+15}{2} = \frac{42}{2} = 21 \text{ cm}$

Calculate the area using Heron's formula

Substitute the values of $s$, $a$, $b$, and $c$ into the area formula.

$\text{Area} = \sqrt{21(21-13)(21-14)(21-15)}$

Simplify the expression

Perform the subtractions and multiply the factors.

$\text{Area} = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{(3 \times 7) \times (2^3) \times 7 \times (2 \times 3)}$

Final Calculation

Group the prime factors to extract the square root.

$\text{Area} = \sqrt{2^4 \times 3^2 \times 7^2} = 2^2 \times 3 \times 7 = 4 \times 21 = 84 \text{ sq cm}$