A triangle has sides of length 10, 10, and 12. 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:

• $$a = 10$$
• $$b = 10$$
• $$c = 12$$

First, calculate the semi-perimeter:

\[ s = \frac{10+10+12}{2} = \frac{32}{2} = 16 \]

Now, apply Heron's formula:

\[ \text{Area} = \sqrt{16(16-10)(16-10)(16-12)} \]

\[ \text{Area} = \sqrt{16(6)(6)(4)} \]

\[ \text{Area} = \sqrt{16 \times 36 \times 4} \]

\[ \text{Area} = \sqrt{2304} \]

\[ \text{Area} = 48 \]

Ответ: $$48$$