Problem:
Regular hexagon ABCDEF has vertices A and C at (0,0) and (7,1), respectively. What is its area?
Answer Choices:
A. 203
B. 223
C. 253
D. 273
E. 50 Solution:
Diagonals AC,CE,EA,AD,CF, and EB divide the hexagon into twelve congruent 30−60−90∘ triangles, six of which make up equilateral △ACE. Because AC=72+12=50, the area of △ACE is 43(50)2=2253. The area of hexagon ABCDEF is 2(2253)=253.
OR
Let O be the center of the hexagon. Then triangles ABC,CDE, and EFA are congruent to triangles AOC,COE, and EOA, respectively. Thus the area of the hexagon is twice the area of equilateral △ACE. Then proceed as in the first solution.