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What is the area of the largest quadrilateral that can be fit into a circle with radius...

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What is the area of the largest quadrilateral that can be fit into a circle with radius 18 cm.

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A quadrilateral is a polygon with 4 sides. The quadrilateral with the largest area that can be fit in a circle is a square.

Let the side of a square be S. The length of the diagonal of the square is `sqrt(S^2 + S^2) = sqrt2*S` . If this is the largest square that can fit into the circle, the radius if the circle is equal to half the length of the diagonal.

`18 = (sqrt 2*S)/2`

=> `sqrt 2*S = 36`

=> `S = 36/sqrt 2`

The area of a square with side `36/sqrt 2` is 648 cm^2

The largest square that can fit into a circle with radius 18 cm is 648 cm^2

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