The cyclic quadrilateral in the circle shown above is a square. The diameter of the circle is 5. Find the area of the green region.


 Jul 2, 2020

Since the square and the circle, share teh circle's diameter, the diagonal of the square is also 5. Therefore the length of the side of the square is \(\frac{5}{√2}\). So the area of the square is \((\frac{5}{√2})^2\) which equals \(\frac{25}{2}\).

Next, we figure out the area of the circle. Since the diameter is 5, the radius is \(\frac{5}{2}\). The area is pi multiplied by the radius sqaured.

So it would be 3.14 (In class, my teacher taught us to use 3.14 as pi) times \(\frac{25}{4}\)which equals at the end, 19.625! If it is incorrect, try typing the answer in terms of pi, see if that helps, or I might've done something wrong.

 Jul 2, 2020

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