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=225​3​. The area of hexagon ABCDEF is 2(225​3​)=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 â–³ACE. Then proceed as in the first solution.