In right triangle ABC, M and N are midpoints of legs AB and BC, respectively. Leg AB is 6 units long, and leg BC is 12 units long. How many square units are in the area of triangle APC?

If we draw median BO, this will split triangle ABC into six smaller triangles that all have the same area

And triangle APC will be composed of two of these

So area of APC = (2/6)Area of ABC = (1/3) Area of ABC = (12 * 6) / 2 * (1/3) = 12