2012 AMC 10B Problems/Problem 19

Solution

The easiest way to find the area would be to find the area of and subtract the areas of and You can easily get the area of because you know and , so 's area is . However, for triangle you don't know However, you can note that triangle is similar to triangle through AA. You see that So, You can do for and Now, you can find the area of which is Now, you do which makes the answer (C). The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.