Problem: The side of an equilateral triangle is s. A circle is inscribed in the triangle and a square is inscribed in the circle. The area of the square is:
Answer Choices:
A. 24s2​
B. 6s2​
C. 6s22​​
D. 6s23​​
E. 3s2​
Solution:
Let r be the radius; h, the altitude; and x, the side of the square.
r=31​h=31​⋅21​s3​=6s3​​∴ Area (square) =x2=2r2=6s2​.