A circle is inscribed in an equilateral triangle of side a. Find the area of any square inscribed in this circle.

Explanation

To find the area of a square inscribed in a circle that is inscribed in an equilateral triangle of side \( a \), we can follow these steps:

### Step 1: Find the radius of the inscribed circle (inradius)
For an equilateral triangle with side length \( a \), the formula for the inradius \( r \) is given by:

\[ r = \frac{a}{2\sqrt{3}} \]
...