Square is a quadrilateral with all sides being equal. The remaining area of the square can be represented as 64-16π.
The area of a square is the product of the length of the square and the width of the square, but since all the sides of the square are equal the area of the square is the square of any of its sides.
[tex]\text{Area of the square} = a^2[/tex]
We know that the four circles are arranged in the square as shown, below, therefore, four times the radius of a circle is the side of the circle. Also, the remaining area of the square is the difference in the area of the square and the area of the four circles, thus, we can write the remaining area of the square,
[tex]\rm Remaining \ Area = \text{Area of the square} - \text{Area of the 4 squares}[/tex]
[tex]= a^2 - 4(\pi r^2)[/tex]
We know that the side of the square is 8 in, while the radius of the 4 circles is 2 in,
[tex]= a^2 - 4(\pi r^2)[/tex][tex]\rm Remaining \ Area = \text{Area of the square} - \text{Area of the 4 squares}[/tex]
[tex]= (8)^2 - 4(\pi 2^2)\\\\= 64 - 4(4\pi)\\\\=64-16\pi[/tex]
Hence, the remaining area of the square can be represented as 64-16π.
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