MNPQ rectangle trapezoid. MP-diagonal. An equilateral QMP triangle with a side of 12 cm

univerkov | May 10, 2021 | education

MNPQ rectangle trapezoid. MP-diagonal. An equilateral QMP triangle with a side of 12 cm. Find the midline of the trapezoid.

Since, by condition, the triangle QMP is equilateral, then MP = MQ = PQ.

Let us draw in the trapezium the height of the RN, which will also be the height, bisector and median of the equilateral triangle QMP.

Then the segment MH = HQ = MQ / 2 = 12/2 = 6 cm.

Since MH is parallel to NP as the base of a trapezoid, and NM is parallel to HP by construction, then MNPH is a rectangle, and then NP = MH = 6 cm.

Determine the length of the middle line of the KE trapezoid.

KE = (NP + MQ) / 2 = (6 + 12) / 2 = 18/2 = 9 cm.

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

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