# In trapezoid ABCD, each side is divided into 4 equal parts. Find the lengths of the segments

July 24, 2021 | education

| **In trapezoid ABCD, each side is divided into 4 equal parts. Find the lengths of the segments КК1 and ММ1, if AD = 3a and BC = 2b.**

Since, by condition, BK = KL = LM = MA, then each of the segments KK1, LL1, MM1 is the middle line of the trapezoids.

LL1 – middle line of trapezoid ABCD.

LL1 = (АD + ВС) / 2 = (3 * a + 2 * b) / 2 = ((3 * a / 2) + b).

KK1 is the middle line of the LBCL1 trapezoid.

KK1 = (LL1 + BC) / 2 = (((3 * a / 2) + b) + 2 * b) / 2 = (3 * a + 6 * b) / 4.

MM1 – middle line of trapezoid ALL1D.

MM1 = (AD + LL1) / 2 = (3 * a + ((3 * a / 2) + b) / 2 = ((6 * a + 3 * a + 2 * b) / 2) / 2 = ( 9 * a + 2 * b) / 4.

Answer:

KK1 = (3 * a + 6 * b) / 4.

MM1 = (9 * a + 2 * b) / 4.

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