ABCD is a rectangular trapezoid. BC = AB = 5 cm, CD = 3 cm. Find the middle line of the trapezoid.

univerkov | September 12, 2021 | education

From the top B of the trapezoid ABCD, lower the height BH.

Since the trapezoid is rectangular, and BH is the height, then the quadrangle BCDH is a rectangle, then BH = CD = 3 s, BC = DH.

In a right-angled triangle ABH, we determine the length of the leg AH.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 25 – 9 = 16.

AH = 4 cm.

Then AD = AH + DH = 4 + 5 = 9 cm.

Let’s define the middle line of the trapezoid.

KM = (BC + AD) / 2 = (5 + 9) / 2 = 14/2 = 7 cm.

Answer: The middle line of the trapezoid is 7cm.

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