[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.14,0:00:02.45,Default,,0000,0000,0000,,- What I want to do in this\Nvideo is get some practice
Dialogue: 0,0:00:02.45,0:00:04.23,Default,,0000,0000,0000,,finding surface areas of figures
Dialogue: 0,0:00:04.23,0:00:07.60,Default,,0000,0000,0000,,by opening them up into\Nwhat's called nets.
Dialogue: 0,0:00:07.60,0:00:09.37,Default,,0000,0000,0000,,And one way to think\Nabout it is if you had
Dialogue: 0,0:00:09.37,0:00:12.25,Default,,0000,0000,0000,,a figure like this, and if\Nit was made out of cardboard,
Dialogue: 0,0:00:12.25,0:00:13.76,Default,,0000,0000,0000,,and if you were to cut it,
Dialogue: 0,0:00:13.76,0:00:17.05,Default,,0000,0000,0000,,if you were to cut it right\Nwhere I'm drawing this red,
Dialogue: 0,0:00:17.05,0:00:20.67,Default,,0000,0000,0000,,and also right over here\Nand right over there,
Dialogue: 0,0:00:20.67,0:00:22.82,Default,,0000,0000,0000,,and right over there and also in the back
Dialogue: 0,0:00:22.82,0:00:24.18,Default,,0000,0000,0000,,where you can't see just now,
Dialogue: 0,0:00:24.18,0:00:26.25,Default,,0000,0000,0000,,it would open up into something like this.
Dialogue: 0,0:00:26.25,0:00:27.72,Default,,0000,0000,0000,,So if you were to open it up,
Dialogue: 0,0:00:27.72,0:00:30.26,Default,,0000,0000,0000,,it would open up into something like this.
Dialogue: 0,0:00:30.26,0:00:32.14,Default,,0000,0000,0000,,And when you open it up, it's much easier
Dialogue: 0,0:00:32.14,0:00:34.31,Default,,0000,0000,0000,,to figure out the surface area.
Dialogue: 0,0:00:34.31,0:00:36.57,Default,,0000,0000,0000,,So the surface area of this figure,
Dialogue: 0,0:00:36.57,0:00:38.55,Default,,0000,0000,0000,,when we open that up,\Nwe can just figure out
Dialogue: 0,0:00:38.55,0:00:40.71,Default,,0000,0000,0000,,the surface area of each of these regions.
Dialogue: 0,0:00:40.71,0:00:41.90,Default,,0000,0000,0000,,So let's think about it.
Dialogue: 0,0:00:41.90,0:00:43.97,Default,,0000,0000,0000,,So what's first of all the surface area,
Dialogue: 0,0:00:43.97,0:00:48.18,Default,,0000,0000,0000,,what's the surface area\Nof this, right over here?
Dialogue: 0,0:00:48.18,0:00:51.45,Default,,0000,0000,0000,,Well in the net, that\Ncorresponds to this area,
Dialogue: 0,0:00:51.45,0:00:56.44,Default,,0000,0000,0000,,it's a triangle, it has a base\Nof 12 and height of eight.
Dialogue: 0,0:00:56.44,0:00:59.90,Default,,0000,0000,0000,,So this area right over\Nhere is going to be one half
Dialogue: 0,0:00:59.90,0:01:03.02,Default,,0000,0000,0000,,times the base, so times 12,
Dialogue: 0,0:01:03.02,0:01:05.80,Default,,0000,0000,0000,,times the height, times eight.
Dialogue: 0,0:01:05.80,0:01:08.20,Default,,0000,0000,0000,,So this is the same\Nthing as six times eight,
Dialogue: 0,0:01:08.20,0:01:12.07,Default,,0000,0000,0000,,which is equal to 48 whatever\Nunits, or square units.
Dialogue: 0,0:01:12.07,0:01:13.96,Default,,0000,0000,0000,,This is going to be units of area.
Dialogue: 0,0:01:13.96,0:01:15.57,Default,,0000,0000,0000,,So that's going to be 48 square units,
Dialogue: 0,0:01:15.57,0:01:17.55,Default,,0000,0000,0000,,and up here is the exact same thing.
Dialogue: 0,0:01:17.55,0:01:19.23,Default,,0000,0000,0000,,That's the exact same thing.
Dialogue: 0,0:01:19.23,0:01:20.26,Default,,0000,0000,0000,,You can't see it in this figure,
Dialogue: 0,0:01:20.26,0:01:21.50,Default,,0000,0000,0000,,but if it was transparent,
Dialogue: 0,0:01:21.50,0:01:24.36,Default,,0000,0000,0000,,if it was transparent,\Nit would be this backside
Dialogue: 0,0:01:24.36,0:01:27.45,Default,,0000,0000,0000,,right over here, but\Nthat's also going to be 48.
Dialogue: 0,0:01:27.45,0:01:29.49,Default,,0000,0000,0000,,48 square units.
Dialogue: 0,0:01:29.49,0:01:32.15,Default,,0000,0000,0000,,Now we can think about the areas of
Dialogue: 0,0:01:32.15,0:01:35.21,Default,,0000,0000,0000,,I guess you can consider\Nthem to be the side panels.
Dialogue: 0,0:01:35.21,0:01:37.67,Default,,0000,0000,0000,,So that's a side panel right over there.
Dialogue: 0,0:01:37.67,0:01:41.38,Default,,0000,0000,0000,,It's 14 high and 10 wide,\Nthis is the other side panel.
Dialogue: 0,0:01:41.38,0:01:45.61,Default,,0000,0000,0000,,It's also this length over here\Nis the same as this length.
Dialogue: 0,0:01:45.61,0:01:47.58,Default,,0000,0000,0000,,It's also 14 high and 10 wide.
Dialogue: 0,0:01:47.58,0:01:51.25,Default,,0000,0000,0000,,So this side panel is\Nthis one right over here.
Dialogue: 0,0:01:51.25,0:01:53.21,Default,,0000,0000,0000,,And then you have one on the other side.
Dialogue: 0,0:01:53.21,0:01:54.92,Default,,0000,0000,0000,,And so the area of each of these
Dialogue: 0,0:01:54.92,0:01:58.74,Default,,0000,0000,0000,,14 times 10, they are 140 square units.
Dialogue: 0,0:01:58.74,0:02:02.24,Default,,0000,0000,0000,,This one is also 140 square units.
Dialogue: 0,0:02:02.24,0:02:04.49,Default,,0000,0000,0000,,And then finally we\Njust have to figure out
Dialogue: 0,0:02:04.49,0:02:06.91,Default,,0000,0000,0000,,the area of I guess you can say the base
Dialogue: 0,0:02:06.91,0:02:10.55,Default,,0000,0000,0000,,of the figure, so this whole\Nregion right over here,
Dialogue: 0,0:02:10.55,0:02:14.26,Default,,0000,0000,0000,,which is this area, which is\Nthat area right over there.
Dialogue: 0,0:02:14.26,0:02:16.74,Default,,0000,0000,0000,,And that's going to be 12 by 14.
Dialogue: 0,0:02:16.74,0:02:21.74,Default,,0000,0000,0000,,So this area is 12 times 14,\Nwhich is equal to let's see.
Dialogue: 0,0:02:21.96,0:02:24.54,Default,,0000,0000,0000,,12 times 12 is 144
Dialogue: 0,0:02:24.54,0:02:28.83,Default,,0000,0000,0000,,plus another 24, so it's 168.
Dialogue: 0,0:02:28.83,0:02:32.84,Default,,0000,0000,0000,,So the total area is\Ngoing to be, let's see.
Dialogue: 0,0:02:32.84,0:02:36.05,Default,,0000,0000,0000,,If you add this one and\Nthat one, you get 96.
Dialogue: 0,0:02:36.05,0:02:37.98,Default,,0000,0000,0000,,96 square units.
Dialogue: 0,0:02:37.98,0:02:40.53,Default,,0000,0000,0000,,The two magenta, I guess\Nyou can say, side panels,
Dialogue: 0,0:02:40.53,0:02:45.08,Default,,0000,0000,0000,,140 plus 140, that's 280. 280.
Dialogue: 0,0:02:45.08,0:02:48.02,Default,,0000,0000,0000,,And then you have this\Nbase that comes in at 168.
Dialogue: 0,0:02:48.02,0:02:50.36,Default,,0000,0000,0000,,We want it to be that same color.
Dialogue: 0,0:02:50.36,0:02:54.69,Default,,0000,0000,0000,,168. One, 68.
Dialogue: 0,0:02:54.69,0:02:56.79,Default,,0000,0000,0000,,Add them all together, and\Nwe get the surface area
Dialogue: 0,0:02:56.79,0:02:58.00,Default,,0000,0000,0000,,for the entire figure.
Dialogue: 0,0:02:58.00,0:03:01.59,Default,,0000,0000,0000,,And it was super valuable\Nto open it up into this net
Dialogue: 0,0:03:01.59,0:03:03.22,Default,,0000,0000,0000,,because we can make sure\Nwe got all the sides.
Dialogue: 0,0:03:03.22,0:03:05.27,Default,,0000,0000,0000,,We didn't have to kinda\Nrotate it in our brains.
Dialogue: 0,0:03:05.27,0:03:07.20,Default,,0000,0000,0000,,Although you could do that as well.
Dialogue: 0,0:03:07.20,0:03:09.78,Default,,0000,0000,0000,,So, with six plus zero plus eight is 14.
Dialogue: 0,0:03:09.78,0:03:14.34,Default,,0000,0000,0000,,Regroup the one ten to the tens\Nplace, there's now one ten.
Dialogue: 0,0:03:14.34,0:03:18.25,Default,,0000,0000,0000,,So one plus nine is ten, plus eight is 18,
Dialogue: 0,0:03:18.25,0:03:22.97,Default,,0000,0000,0000,,plus six is 24, and then you have
Dialogue: 0,0:03:22.97,0:03:25.37,Default,,0000,0000,0000,,two plus two plus one is five.
Dialogue: 0,0:03:25.37,0:03:29.11,Default,,0000,0000,0000,,So the surface area of this figure is 544.
Dialogue: 0,0:03:29.11,0:03:31.26,Default,,0000,0000,0000,,544 square units.