To find the surface area of a pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.
The base of the pyramid is a rectangle with dimensions 12 yd x 12 yd, so its area is (12 yd) x (12 yd) = 144 square yards.
To find the area of each triangular face, we need to find the area of the base of the triangle and multiply it by half the height of the pyramid.
The height of the pyramid can be found using the Pythagorean theorem, since we have a right triangle with legs of length 6 yd and 19 yd.
The height of the pyramid is sqrt((19 yd)^2 - (6 yd)^2) = sqrt(325) yd.
The area of each triangular face is (1/2) x (12 yd) x (sqrt(325) yd) = 6sqrt(325) square yards.
Therefore, the total surface area of the pyramid is 144 square yards + 4 x 6sqrt(325) square yards = 144 + 24sqrt(325) square yards.
So, the surface area of the pyramid is approximately 300.4 square yards.