Find the length of the midline of a rectangular trapezoid with an acute angle of 45

Find the length of the midline of a rectangular trapezoid with an acute angle of 45, which has a smaller side and a smaller base equal to 9.

1. The tops of the trapezoid – A, B, C, D. ∠D = 45 °. AB = BC = 9 units. CH – height. MK is the middle line.

2. CH = AB, BC = AH, since they are the sides of the rectangle opposite each other (opposite).

3. Calculate the length of the segment DH through the tangent ∠D:

CH: DH = tangent ∠D = tangent 45 ° = 1.

DH = 9: 1 = 9 units.

4. АD = АН + DH = 9 + 9 = 18 units of measurement.

5. MK = (BC + AD) / 2 = (9 + 18): 2 = 27: 2 = 13.5 units.

Answer: MK = 13.5 units of measurement.