What’s the Area of a “Pseudo-Square”?

This Week's Fiddler

First, find the radius of the small circle. We can do this because we can determine its relation to the circumference of the small circle, and we know the small sector is similar to the large sector.

Then we find the area of the small circle, add to it the area of the large sector, and subtract from it the area of the small sector.

TODO: Write the actual steps it takes to do that

The final answer is $\frac{1}{2} + \frac{1}{\pi} - \frac{1}{1 + π + \sqrt{1 + π^2}}$, or about 0.6839.

Answer: 0.6839

Extra Credit

Didn't get around to it 😔