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An equilateral triangle is inscribed in a regular hexagon, and a smaller regular hexagon is inscribed inside the triangle so that three of its vertices are each the midpoint of a side of the triangle. What is the ratio of the area the smaller hexagon to the larger hexagon?

 Dec 26, 2018

Here's the image : 




The side of the smaller hexagon is 1/2 that of the larger hexagon = scale factor


Then the ratio of the area of the smaller hexagon to the larger =  (scale factor)^2  =


(1/2)^2   =    1 / 4    =    1  :  4



cool cool cool

 Dec 26, 2018

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