Problem: If P1​P2​P3​P4​P5​P6​ is a tegular hexagon whose apothem (distance from the center to the midpoint of a side) is 2, and Qi​ is the midpoint of side Pi​Pi+1​ for i=1,2,3,4, then the area of quadrilateral Q1​Q2​Q3​Q4​ is
Answer Choices:
A. 6
B. 26​
C. 383​​
D. 33​
E. 43​
Solution:
If C is the center of the hexagon, then the area of Q1​Q2​Q3​Q4​ is the sum of of the areas of the three equilaterat triangles ΛQ1​Q2​C,ΔQ2​Q3​C,ΔQ3​Q4​C each of whose sides have length 2 . Therefore, area Q1​Q2​Q3​Q4​=3(4223​​)=33​.