In an isosceles trapezoid, the height divides the larger base into segments of 5 and 12 cm. Find the midline of the trapezoid.

The middle line of a trapezoid is a segment connecting the midpoints of its lateral sides. It is parallel to the bases and is equal to half of their sum:

m = (a + b) / 2 h.

To do this, you need to find the length of its bases.

Since the length of the smaller base is equal to the segment of the larger base located between the heights, then:

ВС = НК = АD – АН – КD.

Since the trapezoid is isosceles, the segments AH and KD are equal:

AH = KD = 5 cm.

In this way:

НК = НD – КD;

NK = 12 – 5 = 7 cm.

AD = AH + HD;

AD = 5 + 12 = 17 cm.

m = (7 + 17) / 2 = 24/2 = 12 cm.

Answer: The middle line of the trapezoid is 12 cm.