2015 AMC 8 Problems/Problem 21
Problem
In the given figure, hexagon is equiangular, and are squares with areas and respectively, is equilateral and . What is the area of ?
.
Solution 1
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 .
Solution 2
Since , and , . Meanwhile, , and since is equilateral, . If is equiangular, , where is the number of sides of the shape. Adding all the angles around gives , so . Because is right, the area of . Therefore, the answer is . ~strongstephen
Video Solution
~savannahsolver
See Also
2015 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.