2012 AMC 10B Problems/Problem 19

The easiest way to find the area would be to find the area of ABCD and subtract the areas of ABG and CDF. You can easily get the area of ABG because you know AB=6 and AG=15, so ABG's area is 5. However, for triangle CDF, you don't know CF. However, you can note that triangle BEF is similar to triangle CDF through AA. You see that BE/DC=1/3. So, You can do BF+3BF=30 for BF=15/2, and CF=15/2. Now, you can find the area of CDF, which is 135/2. Now, you do 180-225/2, which turns out to be 135/2, which makes the answer (C).