what is the area included between a circle and an inscribed square of side 'a' units
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When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A = π r 2.
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Diagonal of square = √2a
So radius of circle = a/√2
Required area
= π(a/√2)^2 - a^2
= (πa^2)/2 - a^2
= 22a^2/14 - a^2
= 11a^2/7 - a^2
= 4a^2/7
so required area is 4a^2/7 unit^2
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