Math Problems: Hexagon Within Another Hexagon

If you had a smaller hexagon whose vertices are circumscribed by a larger hexagon whose side length is 4, what is the square of the area of the smaller hexagon?

Answer: 972

The side length of the smaller hexagon is 2*sqrt(3). The area of one equilateral triangle is 0.5(bh) = 0.5(3)(2sqrt(3)) = 3sqrt(3). Multiply this by 6 to get the total area of the hexagon, 18sqrt(3). X^2 is then 972.