Calculate the area of a right triangle with sides of 6 in, 8in, and 10 in

1. Identify that the given triangle with sides 6 in, 8 in, and 10 in is a right triangle because it satisfies the Pythagorean theorem:

6^2 + 8^2 = 10^2

2. The formula for the area of a right triangle is:

\text{Area} = \frac{1}{2} \cdot \text{base} \cdot \text{height}

3. Use 6 in as the base and 8 in as the height:

\text{Area} = \frac{1}{2} \cdot 6 \cdot 8 = \frac{1}{2} \cdot 48 = 24 \text{ in}^2

4. Therefore, the area of the triangle is:

24 \text{ in}^2