what is the area of this figure?\n\nif necessary, round your answer to the nearest hundredth.\n\nsquare feet

Explanation:

Step1: Divide the figure into basic shapes

The figure consists of two rectangles and one semicircle.

Step2: Calculate the area of the top rectangle

The top rectangle has a width of $7\text{ ft}$ and a height of $4\text{ ft}$. $$A_{1} = 7 \times 4 = 28\text{ ft}^{2}$$

Step3: Calculate the area of the bottom rectangle

The bottom rectangle has a width of $13\text{ ft}$ and a height of $5\text{ ft}$. $$A_{2} = 13 \times 5 = 65\text{ ft}^{2}$$

Step4: Determine the diameter of the semicircle

The total height on the left is $2 + d + 3$, which must equal the total height on the right, $4 + 5 = 9\text{ ft}$. $$d = 9 - 2 - 3 = 4\text{ ft}$$

Step5: Calculate the area of the semicircle

The radius $r$ is $\frac{4}{2} = 2\text{ ft}$. The area is half of $\pi r^{2}$. $$A_{3} = \frac{1}{2} \times \pi \times 2^{2} = 2\pi \approx 6.28318\text{ ft}^{2}$$

Step6: Sum the areas for the total area

Add the areas of the two rectangles and the semicircle. $$A_{total} = 28 + 65 + 6.28318 = 99.28318\text{ ft}^{2}$$

Step7: Round to the nearest hundredth

Round the total area to two decimal places. $$A_{total} \approx 99.28\text{ ft}^{2}$$

Answer:

99.28 square feet