Cutting a piece of wire

Geometry Level 3

A piece of wire 224 224 inches long is cut into 3 3 pieces in the ratio 1 : 4 : 9 1:4:9 . The shortest piece is bent to form a square. The longest piece is bent to form a regular hexagon. The third piece is bent to form a circle. Which of the following is the sum of the areas (square inches) of the three polygons formed?

2 π ( 8 π + 864 π 3 + 512 ) \dfrac{2}{\pi}(8\pi+864\pi\sqrt{3}+512) 2 π ( 8 π + 431 π 3 + 512 ) \dfrac{2}{\pi}(8\pi+431\pi\sqrt{3}+512) 16 π + 864 π 3 + 512 2 π 16\pi+864\pi\sqrt{3}+\dfrac{512}{2\pi} 2 π ( 8 π + 432 π 3 + 512 ) \dfrac{2}{\pi}(8\pi+432\pi\sqrt{3}+512)

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