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

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