Question

Given: FGKL is a trapezoid, m∠F=90°, m∠K=120°, FK=LK=a Find: The length of midsegment.

Answer 1

(3/4)a

Explanation:

The angle at K is 120°, so the angle at L is its supplement: 60°. That makes triangle FKL an equilateral triangle with a base of FL = a. The vertex at K is centered over the base, so is a/2 from G.

The midsegement length is the average of GK and FL, so is ...

midsegment = (GK +FL)/2 = (a/2 +a)/2

midsegment = (3/4)a