The angle at the smaller base of the trapezoid is 120º, the three sides are 6 cm. Find the middle line of the trapezoid.

We draw from the top B to the height of BH, then in the right-angled triangle ABH the angle ABH = ABC – HBC = 120 – 90 = 30. The leg AH lies opposite the angle 30, and therefore is equal to half the length of the hypotenuse AB.

AH = AB / 2 = 6/2 = 3 cm.

In an isosceles trapezoid, the height drawn to the larger base divides it into two segments, the smaller of which is equal to the half-difference of the bases.

AH = (AD – BC) / 2.

3 = (AD – 6) / 2.

AD = 12 cm.

Let’s define the middle line of the trapezoid.

КР = (ВС + АD) / 2 = (6 + 12) / 2 = 18/2 = 9 cm.

Answer: The length of the middle line is 9 cm.