Final answer:
The surface area of the triangular prism is 196 units squared.
Step-by-step explanation:
To find the surface area of a triangular prism, we need to add the areas of all its faces.
The prism shown above has a triangular base with sides X, Y, and Z units long, and a height of h units. Therefore, the triangular base has an area of ½ XY units squared. The prism also has three rectangular faces, each with a length of h units and a width of X, Y, or Z units, depending on which side it is attached to. Thus, the total area of the rectangular faces is 3hX + 3hY + 3hZ = 3h(X + Y + Z) units squared. Adding the area of the triangular base and the rectangular faces, we get a total surface area of ½ XY + 3h(X + Y + Z) units squared. Now, plugging in the given values for X, Y, Z, and h, we get ½ * 7 * 4 + 3 * 7(7 + 4 + 18) = 98 + 399 = 497 units squared.
However, since the surface area is measured in units squared, we need to use exponents to properly represent the final answer. Therefore, the surface area of the triangular prism is 497 units squared, or 497 units^2.