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- What I want to do in this
video is get some practice
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finding surface areas of figures
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by opening them up into
what's called nets.
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And one way to think
about it is if you had
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a figure like this, and if
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
where I'm drawing this red,
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and also right over here
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,
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
of this, right over here?
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Well in the net, that
corresponds to this area,
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it's a triangle, it has a base
of 12 and height of eight.
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So this area right over
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
thing as six times eight,
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which is equal to 48 whatever
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,
it would be this backside
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right over here, but
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
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,
this is the other side panel.
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It's also this length over here
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
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
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
region right over here,
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which is this area, which is
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,
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
going to be, let's see.
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If you add this one and
that one, you get 96.
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96 square units.
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The two magenta, I guess
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
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
we get the surface area
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for the entire figure.
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And it was super valuable
to open it up into this net
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because we can make sure
we got all the sides.
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We didn't have to kinda
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
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.