To find the surface area of the figure, we first need to find the surface area of each individual shape and then add them together.
Surface area of the rectangular prism:
- Front and back faces: 2(12 ft * 8 ft) = 192 sq ft
- Top and bottom faces: 2(12 ft * 8 ft) = 192 sq ft
- Left and right faces: 2(8 ft * 8 ft) = 128 sq ft
Total surface area of the rectangular prism = 192 + 192 + 128 = 512 sq ft
Surface area of the right triangular prism (not including the hypotenuse):
- Front and back faces: 2(8 ft * h) = 16h sq ft
- Left and right faces: 15 ft * h = 15h sq ft (since the hypotenuse is not visible)
- Top face: 8 ft * 15 ft = 120 sq ft
Total surface area of the right triangular prism = 16h + 15h + 120 = 31h + 120 sq ft
Therefore, the total surface area of the figure is 512 sq ft + 31h + 120 sq ft = 31h + 632 sq ft.