# 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
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## 1 Answer

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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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