In trapezoid ABCD, AD is parallel to BC. Points P, R, and M cut AB into four congruent segments; points Q, S, and N cut CD into four congruent segments. If AD=12 and BC=18, then AD+PQ+RS+MN+BC=?

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One of the standard results about trapezoids is that a line that is parallel to the two bases and bisects the sides has length equal to the arithmetic average of the bases. That is, the length of RS is the average of the lengths of AD and BC: (12+ 18)/2= 30/2= 15. Now apply the same thing to PQ and MN.