Question

A circle is placed in a square with a side length of 16 ft , as shown below. Find the area of the shaded region.

Use 3.14 as pi and don't round.

Answer 1

55.04 ft^2

Explanation:

Well, the area of a circle is πr^2 and since the length of the square is 16, the diameter is 16, meaning the radius is 8. now, it's (3.14)(8^2) which is (3.14)(64). If you multiply those together, you get 200.96. Now, we find the area of the square, which is 16 x 16, which is 256. Now, since we need to find the area of the shaded region, we do (the area of the square)-(the area of the circle). Now, that is 256-200.96=55.04. So, the answer is 55.04ft^2

Answer 2

55.04 ft²

Explanation:

Calculate the area of the square, the area of the circle, then subtract the area of the circle from the area of the square.

Area of square = 16 x 16 = 256 ft²

Area of circle =
`\pi`r²

radius = 16 ÷ 2 = 8

⇒ Area of circle = 3.14 x 8² = 200.96 ft²

Shaded area = 256 - 200.96 = 55.04 ft²