In an isosceles trapezoid, the base angle is 45 degrees and the height is 5., the smaller base is 6, find the large base

In a right-angled triangle CDH, one of the acute angles is 45, then this triangle is also isosceles, CH = DH = 5 cm.

Let’s build another height BK.

Triangles ABK and CDH are rectangular in which AB = CD, since the trapezoid is isosceles, and the angle ABK = CDH, then the triangles ABK and CDH are equal, and therefore AK = DH = 5 cm.

A quadrilateral BСNK rectangle, then КН = ВС = 6 cm.

Base AD = AK + KH + DH = 5 + 6 + 5 = 16 cm.

Answer: The length of the larger base is 16 cm.