Problem:
The equiangular convex hexagon ABCDEF has AB=1,BC=4,CD=2, and DE=4. The area of the hexagon is
Answer Choices:
A. 215​3​
B. 93​
C. 16
D. 439​3​
E. 443​3​
Solution:
Extend FA and CB to meet at X,BC and ED to meet at Y, and DE and AF to meet at Z. The interior angles of the hexagon are 120∘. Thus the triangles XYZ,ABX,CDY, and EFZ are equilateral. Since AB=1,BX=1. Since CD=2,CY=2. Thus XY=7 and YZ=7. Since YD=2 and DE=4,EZ=1. The area of the hexagon can be found by subtracting the areas of the three small triangles from the area of the large triangle:
