![]() So if I’d worked out the perimeter of the base of our prism here and multiplied that by the length of the prism, I get the same answer, but it takes a bit less working out to do. The volume of a triangular prism As we already know that the base of a triangular prism is in the shape of a triangle. So when I work out the overall area of that rectangle, 80 times 32, I still get 2560 square inches. There are two important formulas for a triangular prism, which are surface area and volume. If I were to slide all of those rectangles together to make one big rectangle, the length of the longest side would be 16 plus 30 plus 34, which is 80 inches. So our answer would be the lateral surface area is 2560 square inches, but there’s actually a slightly quicker way of doing the calculation. Now each of the individual links were in inches, so the area is in inches times inches that’s inches squared or squared inches. Use the figure in the volume section above as reference. where l is length, w is width, and h is height. The total surface area is the surface area of all of the faces of a rectangular prism and is given by the formula. Now we could work out the area of each rectangle individually, so 16 times 32, 30 times 32, and 34 times 32, and then add them together, which gives us a total of 2560. The surface area of a rectangular prism can be broken up into two parts: lateral surface area and total surface area. So that adds up to be three different rectangles that make up the sides of our prism. So that’s this area plus this area plus this area. So when we’re asked for the lateral surface area, this means the total area of all the sides of our prism. Now our given figure is a triangular prism, and our base or cross section is a triangle like this, which is repeated all the way through the prism. Determine the lateral surface area of the given figure. The area covered by all the faces of a right triangular prism represents the total surface area.
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