In a rectangular trapezoid, the acute angle is 45, and the lengths of the smaller side and the smaller

In a rectangular trapezoid, the acute angle is 45, and the lengths of the smaller side and the smaller sash are 6. Find the length of the midline.

Let’s build the height of the CH trapezoid DCH.

Quadrangle ABCN is a rectangle, since the trapezoid is rectangular, and CH is its height, then AH = BC = 6 cm, CH = AB = 6 cm.

The right-angled triangle CDH is isosceles, since its acute angle is 45, then DH = CH = 6 cm.

AD = AH + DH = 6 + 6 = 12 cm.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (6 + 12) / 2 = 9 cm.

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