2015 AMC 8 Problems/Problem 21
Contents
Problem
In the given figure hexagon is equiangular,
and
are squares with areas
and
respectively,
is equilateral and
. What is the area of
?
.
Solution
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
.
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.