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