2015 AMC 8 Problems/Problem 21
In the given figure hexagon is equiangular, and are squares with areas and respectively, is equilateral and . What is the area of ?
Clearly, since is a side of a square with area , . Now, since , we have .
Now, is a side of a square with area , so . Since is equilateral, .
Lastly, is a right triangle. We see that , so is a right triangle with legs and . Now, its area is , and our answer is .