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=31h=31⋅21s3=6s3∴ Area (square) =x2=2r2=6s2.