The largest possible circle is cut out of a square whose side length is 12 feet. What will be the approximate area, in square feet, of the remaining board? ( where )

To solve this problem, we first need to find the area of the square and the area of the circle, then subtract the latter from the former.

Step 1: Find the area of the square. The formula for the area of a square is side length squared. So, the area of the square is 12 feet * 12 feet = 144 square feet.

Step 2: Find the diameter and radius of the circle. The largest possible circle that can be cut out of the square will have a diameter equal to the side length of the square. So, the diameter of the circle is 12 feet. The radius of the circle is half the diameter, so the radius is 12 feet / 2 = 6 feet.

Step 3: Find the area of the circle. The formula for the area of a circle is pi * radius squared. So, the area of the circle is pi * (6 feet)^2 = 36pi square feet. Using 3.14 as the value of pi, the area of the circle is approximately 113.04 square feet.

Step 4: Subtract the area of the circle from the area of the square. The area of the remaining board is the area of the square minus the area of the circle. So, the area of the remaining board is 144 square feet - 113.04 square feet = approximately 30.96 square feet.