Question

determine the shaded area.

the shaded area is
(round to two decimal places as needed.)

Explanation:

Find the dimensions of the square

The radius of the inscribed circle is \(r = 3\text{ ft}\).
The side length of the square is equal to the diameter of the circle:

$$s = 2r = 2(3) = 6\text{ ft}$$

Calculate the area of the square and the circle

The area of the square is:

$$A_{\text{square}} = s^2 = 6^2 = 36\text{ sq ft}$$

The area of the circle is:

$$A_{\text{circle}} = \pi r^2 = \pi (3)^2 = 9\pi\text{ sq ft}$$

Calculate the shaded area

Subtract the area of the circle from the area of the square:

$$A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}} = 36 - 9\pi \approx 36 - 28.2743 = 7.7257\text{ sq ft}$$

Rounding to two decimal places gives \(7.73\text{ sq ft}\).

Answer:

Determine the shaded area.

The shaded area is <blank>7.73</blank> <blank>\(\text{ft}^2\)</blank>
(Round to two decimal places as needed.)