In an isosceles trapezoid ABCD Given: CB = 20; AB = 32. Angle A = 60 degrees Find: Perimeter ABCD.

Let’s draw the heights BK, CL. We get two right-angled triangles, consider triangle AKB (angle K is right):
cosA = AK / AB;
AK = cosA * AB;
AK = (1/2) * 32 = 16 cm.
Since the length of AK is equal to the length of LD and is equal to 16 cm, and the length of KL is equal to the length of the smaller base and is equal to 20 cm, then we can find the length of the larger base:
AD = AK + LD + KL = 16 + 16 + 20 = 52 cm.
We can find the perimeter of the trapezoid:
P = 52 + 20 + 32 + 32 = 136 cm.
Answer: the perimeter of this isosceles trapezoid is 136 cm.