WEBVTT 00:00:00.144 --> 00:00:02.449 - What I want to do in this video is get some practice 00:00:02.449 --> 00:00:04.228 finding surface areas of figures 00:00:04.228 --> 00:00:07.605 by opening them up into what's called nets. 00:00:07.605 --> 00:00:09.369 And one way to think about it is if you had 00:00:09.369 --> 00:00:12.247 a figure like this, and if it was made out of cardboard, 00:00:12.247 --> 00:00:13.762 and if you were to cut it, 00:00:13.762 --> 00:00:17.047 if you were to cut it right where I'm drawing this red, 00:00:17.047 --> 00:00:20.666 and also right over here and right over there, 00:00:20.666 --> 00:00:22.825 and right over there and also in the back 00:00:22.825 --> 00:00:24.175 where you can't see just now, 00:00:24.175 --> 00:00:26.247 it would open up into something like this. 00:00:26.247 --> 00:00:27.719 So if you were to open it up, 00:00:27.719 --> 00:00:30.265 it would open up into something like this. 00:00:30.265 --> 00:00:32.145 And when you open it up, it's much easier 00:00:32.145 --> 00:00:34.307 to figure out the surface area. 00:00:34.307 --> 00:00:36.567 So the surface area of this figure, 00:00:36.567 --> 00:00:38.554 when we open that up, we can just figure out 00:00:38.554 --> 00:00:40.713 the surface area of each of these regions. 00:00:40.713 --> 00:00:41.900 So let's think about it. 00:00:41.900 --> 00:00:43.970 So what's first of all the surface area, 00:00:43.970 --> 00:00:48.178 what's the surface area of this, right over here? 00:00:48.178 --> 00:00:51.448 Well in the net, that corresponds to this area, 00:00:51.448 --> 00:00:56.435 it's a triangle, it has a base of 12 and height of eight. 00:00:56.435 --> 00:00:59.898 So this area right over here is going to be one half 00:00:59.898 --> 00:01:03.020 times the base, so times 12, 00:01:03.020 --> 00:01:05.801 times the height, times eight. 00:01:05.801 --> 00:01:08.195 So this is the same thing as six times eight, 00:01:08.195 --> 00:01:12.066 which is equal to 48 whatever units, or square units. 00:01:12.066 --> 00:01:13.959 This is going to be units of area. 00:01:13.959 --> 00:01:15.572 So that's going to be 48 square units, 00:01:15.572 --> 00:01:17.548 and up here is the exact same thing. 00:01:17.548 --> 00:01:19.228 That's the exact same thing. 00:01:19.228 --> 00:01:20.260 You can't see it in this figure, 00:01:20.260 --> 00:01:21.499 but if it was transparent, 00:01:21.499 --> 00:01:24.360 if it was transparent, it would be this backside 00:01:24.360 --> 00:01:27.452 right over here, but that's also going to be 48. 00:01:27.452 --> 00:01:29.492 48 square units. 00:01:29.492 --> 00:01:32.148 Now we can think about the areas of 00:01:32.148 --> 00:01:35.214 I guess you can consider them to be the side panels. 00:01:35.214 --> 00:01:37.668 So that's a side panel right over there. 00:01:37.668 --> 00:01:41.376 It's 14 high and 10 wide, this is the other side panel. 00:01:41.376 --> 00:01:45.614 It's also this length over here is the same as this length. 00:01:45.614 --> 00:01:47.578 It's also 14 high and 10 wide. 00:01:47.578 --> 00:01:51.250 So this side panel is this one right over here. 00:01:51.250 --> 00:01:53.214 And then you have one on the other side. 00:01:53.214 --> 00:01:54.925 And so the area of each of these 00:01:54.925 --> 00:01:58.735 14 times 10, they are 140 square units. 00:01:58.735 --> 00:02:02.243 This one is also 140 square units. 00:02:02.243 --> 00:02:04.491 And then finally we just have to figure out 00:02:04.491 --> 00:02:06.910 the area of I guess you can say the base 00:02:06.910 --> 00:02:10.552 of the figure, so this whole region right over here, 00:02:10.552 --> 00:02:14.256 which is this area, which is that area right over there. 00:02:14.256 --> 00:02:16.743 And that's going to be 12 by 14. 00:02:16.743 --> 00:02:21.743 So this area is 12 times 14, which is equal to let's see. 00:02:21.965 --> 00:02:24.540 12 times 12 is 144 00:02:24.540 --> 00:02:28.830 plus another 24, so it's 168. 00:02:28.830 --> 00:02:32.845 So the total area is going to be, let's see. 00:02:32.845 --> 00:02:36.046 If you add this one and that one, you get 96. 00:02:36.046 --> 00:02:37.984 96 square units. 00:02:37.984 --> 00:02:40.527 The two magenta, I guess you can say, side panels, 00:02:40.527 --> 00:02:45.079 140 plus 140, that's 280. 280. 00:02:45.079 --> 00:02:48.019 And then you have this base that comes in at 168. 00:02:48.019 --> 00:02:50.360 We want it to be that same color. 00:02:50.360 --> 00:02:54.690 168. One, 68. 00:02:54.690 --> 00:02:56.792 Add them all together, and we get the surface area 00:02:56.792 --> 00:02:58.004 for the entire figure. 00:02:58.004 --> 00:03:01.587 And it was super valuable to open it up into this net 00:03:01.587 --> 00:03:03.216 because we can make sure we got all the sides. 00:03:03.216 --> 00:03:05.272 We didn't have to kinda rotate it in our brains. 00:03:05.272 --> 00:03:07.197 Although you could do that as well. 00:03:07.197 --> 00:03:09.775 So, with six plus zero plus eight is 14. 00:03:09.775 --> 00:03:14.337 Regroup the one ten to the tens place, there's now one ten. 00:03:14.337 --> 00:03:18.251 So one plus nine is ten, plus eight is 18, 00:03:18.251 --> 00:03:22.970 plus six is 24, and then you have 00:03:22.970 --> 00:03:25.369 two plus two plus one is five. 00:03:25.369 --> 00:03:29.107 So the surface area of this figure is 544. 00:03:29.107 --> 00:03:31.260 544 square units.