Median of a Trapezoid

The trapezoid P\!ART has m\angle P=x^\circ and m\angle A=2x^\circ. The three congruent sides have lengths s. Find the length of the median in terms of s.

Source: NCTM Mathematics Teacher 2008

SOLUTION

m\angle P+m\angle A+m\angle R+m\angle T=360^\circ
x+2x+2x+x=360^\circ
6x=360^\circ
x=60^\circ
Triangle P\!AB is a 30^\circ-60^\circ-90^\circ triangle with hypotenuse equal s.
P\!B=s/2
Likewise CT=s/2
Median of trapezoid
MN=\dfrac{AR+PT}{2}
=\dfrac{AR+PB+BC+CT}{2}
=\dfrac{s+s/2+s+s/2}{2}
=3s/2

Answer: 3s/2

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About mvtrinh

Retired high school math teacher.
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