SOLUTION: can you please help me solve and leave answer in terms of pie ((( two similar polygons have the scale factor 5:2. The area of the larger polygon is 100. Find the are of the smaller

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Question 198939This question is from textbook geometry
: can you please help me solve and leave answer in terms of pie ((( two similar polygons have the scale factor 5:2. The area of the larger polygon is 100. Find the are of the smaller polygon. ))) This question is from textbook geometry

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

A regular -gon has an area given by:

So if two similar regular polygons have a scale factor of then for a unit length of , the measure of the side of the smaller polygon is and the measure of the side of the larger is and the areas of the two -gons are:

and

So now we can say that:

But we are given that , so:

So:

In general, two similar -gons whose scale factor proportion is have areas that are in proportion . Using this general rule, the area proportion is which is equivalent to and .

Sorry, but has nothing to do with this. Shrug it off and go have a piece of cake.

John