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

Answer

The figure consists of a large rectangle, a small bottom rectangle, and a top quarter-circle.

The large rectangle has a width of $6\text{ ft} + 2\text{ ft} = 8\text{ ft}$ and a height of $7\text{ ft}$. $$A_{1} = 8 \times 7 = 56\text{ ft}^{2}$$

The bottom rectangle has a width of $2\text{ ft}$ and a height of $4\text{ ft}$. $$A_{2} = 2 \times 4 = 8\text{ ft}^{2}$$

The quarter-circle has a radius $r = 3\text{ ft}$. $$A_{3} = \frac{1}{4} \pi r^{2} = \frac{1}{4} \pi (3)^{2} = 2.25\pi \approx 7.0685\text{ ft}^{2}$$

Add the areas of the three components to find the total area. $$A_{total} = 56 + 8 + 7.0685 = 71.0685\text{ ft}^{2}$$

Round the final result to two decimal places. $$A_{total} \approx 71.07\text{ ft}^{2}$$

71.07 square feet