Right triangle ABC has legs of length 12 and 6. Point D is chosen at random within the triangle ABC. What is the probability that the area of triangle ABD is at most 12?
In order for the area of triangle ABD to be at most 12, the height of triangle ABD is at most 2. The height of triangle ABD can be 6, so the probability is 2/6 = 1/3.
+306 
