# In an isosceles trapezoid, the height divides the larger base into segments equal to 6 and 18 cm

In an isosceles trapezoid, the height divides the larger base into segments equal to 6 and 18 cm. find the middle line of the trapezoid.

Let’s call our trapezoid ABCD, where AB, CD are the sides, BC, AD are the bases, BK is the height, then the length of the AK is 6 cm, let’s draw the second height CL, then the length LD is 6 cm, if the trapezoid is isosceles, we find the length KL:
18 – 6 = 12 cm. The length of KL and the length of BC are the same, then the length of BC is 12 cm. The length of AD is equal to the sum of AK and KD:
6 + 18 = 24 cm.
Find the middle line of a trapezoid as a half-sum of the bases:
(BC + AD) / 2 = (12 + 24) / 2 = 18 cm.
Answer: the length of the middle line of the trapezoid is 18 cm.

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