For a circle inscribed in a square what is the ratio of their areas?

For a circle inside a square, the diameter is the same as the side length, and the area of the circle is about 78.54% of the square's area (pi/4).

A(c) = 0.7854 A(s)

The area of the square is L x L. (For a square, L = W).

The area of the circle is PI x R^2, where R = L/2.

Let's express the area of the square using A = L x L = (2R) x (2R) = 4 R^2

So, the ratio of the area of the circle to that of the square is: pi/4 or about 0.7854.