Given:
- The base of a right pyramid is a square with an area of 324 sqm.
- The volume of the pyramid is 1296 cu.m.

We need to find the area of the slant surface of the pyramid.

Approach:
To find the area of the slant surface, we need to first find the slant height of the pyramid. We can then use the slant height and the base length to calculate the area of the slant surface.

Solution:
Step 1: Find the length of the base of the pyramid.
The area of the square base is given as 324 sqm.
Let the length of one side of the square base be 'a'.
So, the area of the square base is given by the formula: Area = a^2 = 324 sqm.

Taking the square root on both sides, we get:
a = √324 = 18 m

The length of the base of the pyramid is 18 m.

Step 2: Find the height of the pyramid.
The volume of the pyramid is given as 1296 cu.m.
The formula for the volume of a pyramid is: Volume = (1/3) * base area * height.

Substituting the given values, we have:
1296 = (1/3) * (324) * height

Simplifying the equation, we get:
height = (1296 * 3) / (324) = 12 m

The height of the pyramid is 12 m.

Step 3: Find the slant height of the pyramid.
The slant height is the hypotenuse of a right-angled triangle formed by the height, the slant height, and half the length of the base.

Using the Pythagorean theorem, we have:
slant height^2 = height^2 + (1/2 * base length)^2
slant height^2 = 12^2 + (1/2 * 18)^2
slant height^2 = 144 + 81 = 225

Taking the square root on both sides, we get:
slant height = √225 = 15 m

The slant height of the pyramid is 15 m.

Step 4: Find the area of the slant surface.
The slant surface area of a pyramid is given by the formula: Area = (1/2) * base perimeter * slant height.

The base perimeter of a square is given by the formula: Perimeter = 4 * side length.

Substituting the given values, we have:
Perimeter = 4 * 18 = 72 m
Slant height = 15 m

Using the formula, we have:
Area = (1/2) * 72 * 15 = 540 sqm

Therefore, the area of the slant surface of the pyramid is 540 sqm.

Answer:
The area of the slant surface is 540 sqm. Hence, option (c) is the correct answer.