Question

a rectangle is removed from a right triangle to create the shaded region shown below. find the area of the shaded region. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of large triangle

The right triangle has legs of length $4\,\text{m} + 5\,\text{m} = 9\,\text{m}$ and $2\,\text{m} + 3\,\text{m} = 5\,\text{m}$. The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.
$$\frac{1}{2} \times 9 \times 5 = 22.5\,\text{m}^2$$

Step2: Calculate area of removed rectangle

The rectangle has length $3\,\text{m}$ and width $2\,\text{m}$. The area of a rectangle is $\text{length} \times \text{width}$.
$$3 \times 2 = 6\,\text{m}^2$$

Step3: Subtract rectangle area from triangle area

Subtract the area of the removed rectangle from the area of the large triangle to get the shaded area.
$$22.5 - 6 = 16.5\,\text{m}^2$$

Answer:

$16.5\,\text{square meters}$