   What is the ratio of the area of big pentagon and small pentagon in the following image?

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What is the ratio of the area of big pentagon and small pentagon in the following image?  posted Jul 5, 2018

The area of the pentagon are proportional to the square of its sides.
So if Big Pentagon has side a
Then we can find the side of Small Pentagon as = (a/4)*((5^0.5) - 1)^2 by knowing that the internal angles of a Regular Pentagon is 108 degrees and Basic Trignometry.
Now required ratio = [Area of Big Pentagon / Area of Small Pentagon]
= a^2/((a/4)^2*(((5^0.5) - 1)^2)^2)
= 2 / ( 7 - (3*5^0.5)). answer Jul 6, 2018

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