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<u>Given:</u>
Each circle has a diameter of 2 inches each.
The outer square has a side length of 4 inches and the square ABCD has a side length of 2 inches.
<u>To find:</u>
The area of the shaded region.
<u>Solution:</u>
Each circle has a diameter of 2 inches. The square ABCD is at the center of each circle so it has a side length of 1 inch.
To determine the area of the shaded region, we subtract the area of the quarter-circles in the square ABCD from the area of the square ABCD.
The area of a quarter-circle
All the quarter-circles have a radius of 1 inch.
The area of 1 quarter-circle
The area of 4 quarter-circles
So the area of the quarter-circles in the square ABCD is 3.1514 square inches.
The area of a square
The area of square ABCD
The area of the shaded region
The area of the shaded region is 0.8585 square inches.