ratio of the green area to the red area
Geometry
Level
2
All arcs shown in the figure above are equal semi-circles. What is the ratio of the green area to the red area?
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1 solution
Let the diameter of the semicircle is d. The regular hexagon area is the sum of red area and the green area, A = 3(d^2 sin 60) = 1.5√3 d^2 .The green area = (3/8)π d^2 . The ratio of the green area to the red area = [(3/8)π d^2]/ [1.5√3 d^2 - (3/8)π d^2 ] = π/[4√3 – π]