To find the area of a right triangle with given leg lengths, you can follow these steps:
1. Identify the lengths of the legs of the right triangle.
- Leg 1: 30 inches
- Leg 2: 10 inches
2. Use the formula for the area of a right triangle:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
In this formula, the base and the height of the right triangle are the lengths of the two legs.
3. Substitute the given values into the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times 30 \, \text{in} \times 10 \, \text{in}
\][/tex]
4. Perform the multiplication:
[tex]\[
30 \times 10 = 300
\][/tex]
5. Divide the product by 2:
[tex]\[
\frac{300}{2} = 150
\][/tex]
6. The area calculated is 150 square inches. Since the problem asks for the area to be rounded to the nearest whole unit squared, you check if rounding is necessary. In this case, 150 is already a whole number.
Therefore, the area of the right triangle is:
[tex]\[
150\, \text{in}^2
\][/tex]
Hence, the area of the right triangle with legs of 30 inches and 10 inches, rounded to the nearest whole unit squared, is 150 in^2.
