A triangle has sides of length 7, 8, and 9. 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:

• $$a = 7$$
• $$b = 8$$
• $$c = 9$$

First, calculate the semi-perimeter:

\[ s = \frac{7+8+9}{2} = \frac{24}{2} = 12 \]

Now, apply Heron's formula:

\[ \text{Area} = \sqrt{12(12-7)(12-8)(12-9)} \]

\[ \text{Area} = \sqrt{12(5)(4)(3)} \]

\[ \text{Area} = \sqrt{12 \times 60} \]

\[ \text{Area} = \sqrt{720} \]

\[ \text{Area} = \sqrt{144 \times 5} = 12\sqrt{5} \]

Ответ: $$12\sqrt{5}$$