WEBVTT 00:00:01.660 --> 00:00:12.390 Find the total surface area of a rectangular prism with length 13 centimetres, width three centimetres, and height three centimetres. 00:00:15.320 --> 00:00:17.620 We’re looking for the surface area. 00:00:19.210 --> 00:00:25.330 Surface area is the amount of space covering the outside of a three-dimensional shape. 00:00:27.880 --> 00:00:46.150 With a rectangular prism that could look something like this of length of 13 centimetres, a width of three centimetres, and a height of three centimetres. 00:00:48.380 --> 00:00:52.350 This rectangular prism has six sides. 00:00:53.640 --> 00:01:01.360 To find the surface area, we need to find the area of each of the six sides and then add them together. 00:01:03.370 --> 00:01:06.560 Let’s start with the area of this piece on the end. 00:01:08.820 --> 00:01:14.570 This piece has a length of three centimetres and a height of three centimetres. 00:01:16.020 --> 00:01:24.720 We multiply three centimetres by three centimetres, which gives us nine centimetres squared. 00:01:27.320 --> 00:01:37.710 We also know that if our right end is nine centimetres squared, then our left end will be the same amount; they have the same area. 00:01:39.670 --> 00:01:43.910 So we have another side; that’s nine centimetres squared. 00:01:44.740 --> 00:01:47.960 We have four remaining sides to find the area. 00:01:50.150 --> 00:01:55.650 Next, we can find the area of the base of the bottom of this rectangular prism. 00:01:57.810 --> 00:02:06.900 It’s in the shape of a rectangle; its length is 13 centimetres and its width is three centimetres. 00:02:08.240 --> 00:02:11.590 We multiply 13 times three to find the area. 00:02:12.880 --> 00:02:17.570 The area of the base would be 39 centimetres squared. 00:02:18.910 --> 00:02:25.470 The base, the bottom, of this rectangle is a congruent rectangle to the top. 00:02:25.990 --> 00:02:32.790 So we know that the top of this rectangular prism has the same area as the bottom. 00:02:35.050 --> 00:02:39.570 The top rectangle will also be 39 centimetres squared. 00:02:41.400 --> 00:02:46.910 We’ve now found the area of four out of the six sides; we have two sides to go. 00:02:49.250 --> 00:02:54.650 We can finally find the area of the front side, which is a rectangle. 00:02:56.410 --> 00:03:03.810 This rectangle has a length of 13 centimetres and a height of three centimetres. 00:03:05.560 --> 00:03:17.200 We multiply 13 times three to find the area; 13 times three is 39 centimetres squared since we’re dealing with area. 00:03:19.400 --> 00:03:28.060 The back rectangle, the one we’ve shaded in yellow, would have the same area as the front rectangle; they are congruent. 00:03:30.160 --> 00:03:37.040 This means that our sixth and final side has an area of 39 centimetres squared. 00:03:38.860 --> 00:03:45.040 To find the total surface area, we need to add the areas of all six of these sides together. 00:03:47.070 --> 00:04:00.420 Nine plus nine for the two end pieces is 18 centimetres squared; 39 centimetres squared plus 39 centimetres squared equals 78 centimetres squared. 00:04:01.640 --> 00:04:18.070 And we have that problem repeated again: 39 plus 39 equals 78 centimetres squared; 18 plus 78 plus 78 equals 174 centimetres squared. 00:04:19.630 --> 00:04:26.360 174 centimetres squared is the total surface area of this rectangular prism.