WEBVTT
00:00:00.600 --> 00:00:03.600
Determine the lateral surface area of the given figure.
00:00:04.280 --> 00:00:13.520
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.
00:00:13.960 --> 00:00:20.160
So when we’re asked for the lateral surface area, this means the total area of all the sides of our prism.
00:00:20.600 --> 00:00:26.000
So that’s this area plus this area plus this area.
00:00:26.360 --> 00:00:31.240
So that adds up to be three different rectangles that make up the sides of our prism.
00:00:31.760 --> 00:00:48.440
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.
00:00:48.920 --> 00:00:57.160
Now each of the individual links were in inches, so the area is in inches times inches; that’s inches squared or squared inches.
00:00:57.720 --> 00:01:09.440
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.
00:01:09.800 --> 00:01:22.520
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.
00:01:22.880 --> 00:01:34.400
So when I work out the overall area of that rectangle, 80 times 32, I still get 2560 square inches.
00:01:34.920 --> 00:01:45.600
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.