The surface area of the figure can be calculated by finding the surface area of each individual face and adding them together.
Surface area of rectangular prism = 2lw + 2lh + 2wh
= 2(12)(8) + 2(12)(8) + 2(8)(8)
= 192 + 192 + 128
= 512 ft^2
Surface area of triangular prism = base area + lateral area
= 1/2 * base * height + perimeter of base * height
= 1/2 * 8 * 15 + (8 + 15 + 17) * h
= 60 + 40h
Total surface area = 512 + (60 + 40h)
= 572 + 40h ft^2
Therefore, the surface area of the figure is 572 + 40h square feet.