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Finding surface area using net

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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.
Title:
Finding surface area using net
Description:

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Video Language:
English
Team:
Khan Academy
Duration:
03:34

English subtitles

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