If X = 8 units, Y = 12 units, Z = 17 units, and h = 5 units, what is the surface area of the triangular prism shown above?
A. 468 square units
B. 510 square units
C. 596 square units
D. 536 square units
To find the surface area of a triangular prism, we need to find the areas of the three rectangles and the two triangles, and then add them together.
The three rectangles have dimensions X by Z, Y by Z, and X by Y.
Rectangle 1: 8 x 17 = 136 square units
Rectangle 2: 12 x 17 = 204 square units
Rectangle 3: 8 x 12 = 96 square units
The two triangles have base X and height h, and base Y and height h.
Triangle 1: (1/2) x 8 x 5 = 20 square units
Triangle 2: (1/2) x 12 x 5 = 30 square units
Adding all the areas together:
136 + 204 + 96 + 20 + 30 = 486 square units
Therefore, the surface area of the triangular prism is 486 square units.
None of the given options match, but the closest one is A. 468 square units.