It is given in the question that,

Perimeter of an isosceles triangle = 32 cm

Let us assume the sides of the triangle be a, b, c and a = b

We know that,

Perimeter = a + b + c

32 = a + b + c

32 = a + a + c

32 = 2a + c (i)

According to the condition given in the question, we have:

a: c = 3: 2

So, a = 3x and c = 2x

Now putting values of a and c in (i), we get

2 × 3x + 2x = 32

6x + 2x = 32

8x = 32

x =

x = 4

Thus, a = 3 × 4 = 12 cm

b = 12 cm

c = 2 × 4 = 8 cm

Now, s =

=

= 16 cm

Area of triangle =

=

=

= 4 × 4 × 2

= 32 cm²