# Find the area of the Grayed triangle Given the following Figure

Can you help me find the area of the gray triangle in the given figure. I'm having a hard time finding the base value of the triangle, I've managed to find the sides for the big triangle but not for the greyed area. Thanks in advance to those that will help.

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You need something that determines the location of $C$. Without that, you can't determine the area. –  Daniel Fischer Jan 16 at 16:38

As mentioned in the comments, there simply isn't enough information. All you know about the grayed triangle is that it is a right triangle with one of its legs having length $4,$ and the other having length somewhere between $0$ and $4\sqrt3.$ With only this information, the best we can conclude is that the grayed triangle can have any area between $0$ and $8\sqrt3.$ (And I do mean any such area. All we have to do is position $C$ appropriately.)