Problem: If P1βP2βP3βP4βP5βP6β is a tegular hexagon whose apothem (distance from the center to the midpoint of a side) is 2, and Qiβ is the midpoint of side PiβPi+1β for i=1,2,3,4, then the area of quadrilateral Q1βQ2βQ3βQ4β is
Answer Choices:
A. 6
B. 26β
C. 383ββ
D. 33β
E. 43β
Solution:
If C is the center of the hexagon, then the area of Q1βQ2βQ3βQ4β is the sum of of the areas of the three equilaterat triangles ΞQ1βQ2βC,ΞQ2βQ3βC,ΞQ3βQ4βC each of whose sides have length 2 . Therefore, area Q1βQ2βQ3βQ4β=3(4223ββ)=33β.