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- What I want to do in this[br]video is get some practice

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finding surface areas of figures

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by opening them up into[br]what's called nets.

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And one way to think[br]about it is if you had

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a figure like this, and if[br]it was made out of cardboard,

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and if you were to cut it,

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if you were to cut it right[br]where I'm drawing this red,

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and also right over here[br]and right over there,

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and right over there and also in the back

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where you can't see just now,

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it would open up into something like this.

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So if you were to open it up,

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it would open up into something like this.

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And when you open it up, it's much easier

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to figure out the surface area.

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So the surface area of this figure,

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when we open that up,[br]we can just figure out

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the surface area of each of these regions.

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So let's think about it.

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So what's first of all the surface area,

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what's the surface area[br]of this, right over here?

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Well in the net, that[br]corresponds to this area,

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it's a triangle, it has a base[br]of 12 and height of eight.

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So this area right over[br]here is going to be one half

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times the base, so times 12,

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times the height, times eight.

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So this is the same[br]thing as six times eight,

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which is equal to 48 whatever[br]units, or square units.

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This is going to be units of area.

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So that's going to be 48 square units,

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and up here is the exact same thing.

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That's the exact same thing.

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You can't see it in this figure,

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but if it was transparent,

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if it was transparent,[br]it would be this backside

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right over here, but[br]that's also going to be 48.

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48 square units.

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Now we can think about the areas of

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I guess you can consider[br]them to be the side panels.

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So that's a side panel right over there.

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It's 14 high and 10 wide,[br]this is the other side panel.

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It's also this length over here[br]is the same as this length.

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It's also 14 high and 10 wide.

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So this side panel is[br]this one right over here.

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And then you have one on the other side.

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And so the area of each of these

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14 times 10, they are 140 square units.

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This one is also 140 square units.

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And then finally we[br]just have to figure out

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the area of I guess you can say the base

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of the figure, so this whole[br]region right over here,

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which is this area, which is[br]that area right over there.

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And that's going to be 12 by 14.

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So this area is 12 times 14,[br]which is equal to let's see.

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12 times 12 is 144

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plus another 24, so it's 168.

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So the total area is[br]going to be, let's see.

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If you add this one and[br]that one, you get 96.

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96 square units.

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The two magenta, I guess[br]you can say, side panels,

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140 plus 140, that's 280. 280.

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And then you have this[br]base that comes in at 168.

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We want it to be that same color.

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168. One, 68.

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Add them all together, and[br]we get the surface area

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for the entire figure.

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And it was super valuable[br]to open it up into this net

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because we can make sure[br]we got all the sides.

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We didn't have to kinda[br]rotate it in our brains.

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Although you could do that as well.

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So, with six plus zero plus eight is 14.

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Regroup the one ten to the tens[br]place, there's now one ten.

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So one plus nine is ten, plus eight is 18,

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plus six is 24, and then you have

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two plus two plus one is five.

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So the surface area of this figure is 544.

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544 square units.