1999 AHSME Problems/Problem 23
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Problem
The equiangular convex hexagon 
has 
and 
The area of the hexagon is
Solution
Equiangularity means that each internal angle must be exactly 
.
The information given by the problem statement looks as follows:
We can now place this incomplete polygon onto a triangular grid, finish it, compute its area in unit triangles, and multiply the result by the area of the unit triangle.
We see that the figure contains 
unit triangles, and therefore its area is 
.
See also
| 1999 AHSME (Problems) | ||
| Preceded by Problem 24 | Followed by Problem 26 | |
| 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 • 26 • 27 • 28 • 29 • 30 | ||
