Solution:
First, let's find the surface area of the triangular prism.
- 2(1/2 x 8 x 12) + 2(10 x 6) + (12 x 6) = Surface area of triangular prism
- => (8 x 12) + 2(60) + (72) = Surface area of triangular prism
- => (96) + 120 + 72 = Surface area of triangular prism
- => 96 + 192 = Surface area of triangular prism
- => 288 ft² = Surface area of triangular prism
Now, let's find the surface area of the rectangular prism.
- 2(18 x 9) + 2(6 x 9) + 2(6 x 18)
- => 2(162) + 2(54) + 2(108)
- => 324 + 108 + 216
- => 2(324) = 648 ft²
Now, add both the surface areas to find the surface area of the figure.
- 288 + 648 = Surface area of figure
- => 936 ft² = Surface area of figure
The surface area of the figure is 936 ft².