Math Help - Area of Inscribed Figures

1. Area of Inscribed Figures

Which occupies a larger percentage of the area compared to the figure containing it: a circle inscribed in a square or a square inscribed in a circle? Assume that the inscribed figures are tangent to the outside figures. Explain.

2. Hi

The area of a square with length a is $A_{square} = a^2$

The diameter of the circle tangent to the square is a. Its area is $A_{circle} = \pi\frac{a^2}{4}$

The ratio of the 2 areas is $\frac{A_{circle}}{A_{square}} = \frac{\pi}{4} = 78.5$%

3. Thank you! I had gotten that far as well... I should have specified earlier, I am stuck with the other figure. When you have a square inscribed in a circle, how do you determine the percentage of the circle the square takes up???

4. The length of the diagonal of the square is $a\:\sqrt{2}$
So is the diameter of the large circle