s = surface area of side (square inches)

b = surface area of base (square inches)

The surface area of the pyramid can be expressed as:  4s + b

The surface area of the base is simply 6^2 = 36 square inches.

To find the surface area of one of the triangular faces, we use the Pythagorean Theorem to find the height of the face.

The tip of the pyramid is above the center of the base, or 3 inches inward.  The height from the base to the tip is 4 inches.  Using 3^2 + 4^2 = c^2, we find that c, the height of each face, is equal to 5 inches.

Now we use (1/2)*base*height to find the surface area of one face:  (1/2)*6*5 = 15 square inches.

Finally, add up the areas of the base and faces:  4(15) + 36 = 96 square inches