Trapezoid Question Regarding Congruent Segments

Oct 2017
4
0
Gravity Falls, Oregon
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=?

tr.JPG

Can somebody help me with this question? Thank you!
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
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.