Parts of a pentagon have areas $x,y,z$ as shown in the picture. Given the area $x$, find the areas $y$ and $z$ and the area of the entire pentagon.
Problem
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Tags: geometry
mop
09.04.2021 07:30
So ABCDE can be any convex pentagon?
jasperE3
09.04.2021 15:03
Any convex pentagon such that the areas labeled with the same letters are equal.
mop
09.04.2021 21:17
Well, then I'll just assume that its regular then Is the answer going to be clean?
Yeetopedia
09.04.2021 21:33
we can use similar polygons. We realize that the polygon with area $x$ is similar to the pentagon. We can a,so notice that the $z$’s ams $y$’s form a circle around $x$, with five zs and five ys. So similarly in the pentagon $x$, there will be 5 zs and five ys, but the ys and zs are $\frac{1}{5}$ each of the original zs and ys in the larger pentagon. Now I’m confused if there is a specific value of $x$, not given in the question?
sargamsujit
09.04.2021 21:37
do some golden gnomon and golden triangle stuff, will try to write up a sol
mop
09.04.2021 21:40
Actually solving the problem isn't that hard, its just the calculations that are a bit tricky.