The acute angle of a rectangular trapezoid is 45 degrees. Determine its midline if the smaller

univerkov | March 8, 2021 | education

The acute angle of a rectangular trapezoid is 45 degrees. Determine its midline if the smaller diagonal and the larger side are equal and the smaller base is 12 cm.

Since the smaller diagonal AC is equal to the larger lateral side of the CD, the triangle ACD is isosceles with the base AD.

Let us construct the height of CH, which is also the median in an isosceles triangle, then AH = DH = AD / 2.

Quadrangle ABCН is a rectangle, then AH = BC = 12 cm, AD = 2 * BC = 2 * 12 = 24 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (12 + 24) / 2 = 36/2 = 18 cm.

Answer: The length of the middle line is 18 cm.

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