A square is cut out of a circle whose diameter is approximately 11 feet. What is the approximate area (shaded region) of the remaining portion of the circle in square feet? (where)

the remaining area is 34.53 ft²

Step-by-step explanation:

assuming that the square that is cut out is the maximum area square that can be cutted from the circle, then this square has a diagonal equal to the diameter of the circle. Then denoting D as the diameter and L as the side length of the square, we have from Pythagoras

D² = L² + L² = 2*L² = 2 * Area of the square

Area of the square = D²/2

Also the area of a circle with diameter D is

Area of the circle = π*D²/4

thus the remaining area after cutting out the square is

Remaining area = Area of the circle - Area of the square = π*D²/4 - D²/2 = (π-2) / 4 * D²

replacing values

Remaining area = (π-2) / 4 * D² = (π-2) / 4 * (11 ft) ² = 34.53 ft²

thus the remaining area is 34.53 ft²

Note:

If the square is other than the one calculated, the remaining area will be more than 34.53 ft²