To find the total surface area of the regular pyramid, we need to determine the area of each face and then sum them up.

1. Area of the Base:
Since the base is a square, we can find its area by multiplying the lengths of its sides. Let's assume the length of each side of the base square is "a". Therefore, the area of the base is given by:
Area of Base = a * a = a^2

2. Area of the Lateral Faces:
The regular pyramid has four lateral faces, which are triangles. To find the area of each lateral face, we need to calculate the area of one of the triangles and multiply it by 4.

2.1. Height of the Triangle:
The height of the triangle can be found using the Pythagorean theorem. The height, h, is the perpendicular distance from the apex of the pyramid to the base. Given that the height of the pyramid is 3 cm, and the length of the side of the base is "a", we can create a right-angled triangle with the height, base, and the length from the apex to one of the vertices of the base. By applying the Pythagorean theorem, we get:
h^2 + (a/2)^2 = 3^2
h^2 + a^2/4 = 9
h^2 = 9 - a^2/4
h = sqrt(9 - a^2/4)

2.2. Area of the Triangle:
The area of a triangle can be found using the formula:
Area of Triangle = (1/2) * base * height

Since the base of the triangle is equal to the side length of the square base, which is "a", and the height is given by h, the area of the triangle is:
Area of Triangle = (1/2) * a * h = (1/2) * a * sqrt(9 - a^2/4)

3. Total Surface Area:
The total surface area of the regular pyramid is the sum of the areas of the base and the four lateral faces.

Total Surface Area = Area of Base + 4 * Area of Triangle
Total Surface Area = a^2 + 4 * (1/2) * a * sqrt(9 - a^2/4)
Total Surface Area = a^2 + 2 * a * sqrt(9 - a^2/4)

We are given that all five faces of the pyramid have the same area. This implies that the area of each face is equal to the area of the base.

a^2 + 2 * a * sqrt(9 - a^2/4) = a^2
2 * a * sqrt(9 - a^2/4) = 0
a * sqrt(9 - a^2/4) = 0

Since the length of a side cannot be zero, we can ignore the second equation. Therefore, the area of the base is zero. This implies that the pyramid cannot exist.

Hence, the given question is invalid as it leads to an impossible scenario.