Given:
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.
To find:
The area of the shaded region.
Solution:
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 [tex]=\frac{\pi r^{2} }{4} .[/tex]
All the quarter-circles have a radius of 1 inch.
The area of 1 quarter-circle [tex]=\frac{\pi r^{2} }{4} = \frac{\pi (1^{2}) }{4} = \frac{3.1415}{4} .[/tex]
The area of 4 quarter-circles [tex]=4(\frac{3.1415}{4}) = 3.1415.[/tex]
So the area of the quarter-circles in the square ABCD is 3.1514 square inches.
The area of a square [tex]= a^{2} .[/tex]
The area of square ABCD [tex]=2^{2} =4.[/tex]
The area of the shaded region [tex]=4-3.1415=0.8585.[/tex]
The area of the shaded region is 0.8585 square inches.
The area can be defined as the space occupied by a flat shape or the surface of an object.
The area of shaded region is 0.86 square inch.
The area of shaded portion is, subtract area of four parts of circle from area of small square.
From figure,
It is observed that, diameter of circle is 2 inch, so that radius of circle is 2/2= 1 inch.
Area of small square is computed as,
[tex]Area=2*2=4inch^{2}[/tex]
Area of four [tex]\frac{1}{4} th[/tex] part of circle = area of one complete circle.
Area of circle is computed as;
[tex]Area=\pi r^{2}=\pi (1)^{2} =\pi inch^{2}[/tex]
So that, Area of shaded region is,
[tex]=4-\pi\\\\=4-3.14=0.86inch^{2}[/tex]
Hence, the area of shaded region is 0.86 square inch.
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