Answer:
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
