Question

find the area to the nearest square foot of the shaded region below, consisting of a square with a circle cut out of it. use 3.14 as an approximation for π. image of square with inscribed circle (diameter 10 ft) options: 54 square feet, 79 square feet, 214 square feet, 22 square feet. the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.

Explanation:

Step1: Calculate area of square

The side length of the square is equal to the diameter of the circle, which is 10 ft. The area of a square is side length squared, so $A_{square} = 10^2 = 100$ square feet.

Step2: Calculate area of circle

The radius of the circle is half of the diameter, so $r = \frac{10}{2} = 5$ ft. The area of a circle is $A_{circle} = \pi r^2$. Using $\pi \approx 3.14$, we get $A_{circle} = 3.14 \times 5^2 = 3.14 \times 25 = 78.5$ square feet.

Step3: Calculate area of shaded region

The shaded area is the area of the square minus the area of the circle, so $A_{shaded} = A_{square} - A_{circle} = 100 - 78.5 = 21.5$ square feet, which rounds to 22 square feet.

Answer:

22 square feet