Question

A circle is placed in a square with a side length of 8ft, as shown below. Find the area of the shaded region.

Use the value 3.14 for , and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

Explanation:

To find the area of the shaded region, we must first find the area of the square. The side length of the square is 8ft, so the area is 8ft x 8ft = 64 square feet.

Next, we need to find the area of the circle. The diameter of the circle is the same as the side length of the square, which is 8ft. Therefore, the radius of the circle is half of the diameter, which is 4ft.

Using the formula for the area of a circle, we get:

Area of circle = π x (radius)^2
Area of circle = 3.14 x (4ft)^2
Area of circle = 3.14 x 16ft^2
Area of circle = 50.24 square feet

Now, we can find the area of the shaded region by subtracting the area of the circle from the area of the square:

Area of shaded region = Area of square - Area of circle
Area of shaded region = 64 square feet - 50.24 square feet
Area of shaded region = 13.76 square feet

Therefore, the area of the shaded region is 13.76 square feet.