The first term (a) of the arithmetic progression (AP) is 11 and the fourth term is 32.

In an AP, the nth term is given by a + (n-1)d, where d is the common difference.

So, we can write: 
a + 3d = 32
Given that a = 11, we can substitute this into the equation to find d:
11 + 3d = 32
3d = 32 - 11
3d = 21
d = 21 / 3
d = 7

The sum S of the first n terms of an AP is given by the formula:
S = n/2 * (2a + (n-1)d)

Substituting n = 9 (since we want the sum of the first nine terms), a = 11, and d = 7 into this formula gives:

S = 9/2 * (2*11 + (9-1)*7)
S = 9/2 * (22 + 56)
S = 9/2 * 78
S = 351