To find the lateral surface area of the triangular prism, we need to find the area of the net of the prism.
First, we need to find the area of the three rectangles that make up the net. The two smaller rectangles have dimensions of 12 inches by 14 inches, so their areas are:
2 * (12 inches * 14 inches) = 2 * 168 = 336 square inches
The larger rectangle has dimensions of 12 inches by 5 inches, so its area is:
12 inches * 5 inches = 60 square inches
Now, we need to find the area of the two right triangles on the net. The base of each triangle is 12 inches, and the height is 5 inches, so the area of each triangle is:
1/2 * (12 inches * 5 inches) = 1/2 * 60 = 30 square inches
Since there are two triangles, the total area of the triangles is 2 * 30 = 60 square inches
Adding all the areas together, we get:
336 square inches + 60 square inches + 60 square inches = 456 square inches
Therefore, the lateral surface area of the triangular prism is 456 square inches.