A triangle has sides of length 13, 14, and 15. Use Heron's formula to find the area.

Heron's formula for the area of a triangle with sides $$a, b, c$$ is: Area $$= \sqrt{s(s-a)(s-b)(s-c)}$$, where $$s$$ is the semi-perimeter, $$s = \frac{a+b+c}{2}$$.

Given:

• $$a = 13$$
• $$b = 14$$
• $$c = 15$$

First, calculate the semi-perimeter:

\[ s = \frac{13+14+15}{2} = \frac{42}{2} = 21 \]

Now, apply Heron's formula:

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

\[ \text{Area} = \sqrt{21(8)(7)(6)} \]

\[ \text{Area} = \sqrt{21 \times 336} \]

\[ \text{Area} = \sqrt{7056} \]

\[ \text{Area} = 84 \]

Ответ: $$84$$