WEBVTT

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What I want to do in this video
is a fairly straightforward

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primer on perimeter and area.

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And I'll do perimeter
here on the left,

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and I'll do area
here on the right.

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And you're probably pretty
familiar with these concepts,

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but we'll revisit it
just in case you are not.

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Perimeter is
essentially the distance

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to go around something
or if you were

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to put a fence around
something or if you

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were to measure-- if you were to
put a tape around a figure, how

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long that tape would be.

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So for example, let's
say I have a rectangle.

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And a rectangle is a figure that
has 4 sides and 4 right angles.

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So this is a
rectangle right here.

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I have 1, 2, 3, 4 right angles.

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And it has 4 sides,
and the opposite sides

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are equal in length.

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So that side is going to be
equal in length to that side,

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and that side is equal
in length to that side.

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And maybe I'll label the
points A, B, C, and D.

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And let's say we
know the following.

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And we know that
AB is equal to 7,

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and we know that
BC is equal to 5.

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And we want to know, what
is the perimeter of ABCD?

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So let me write it down.

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The perimeter of
rectangle ABCD is just

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going to be equal to the sum
of the lengths of the sides.

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If I were to build a fence, if
this was like a plot of land,

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I would just have
to measure-- how

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long is this side
right over here?

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Well, we already know
that's 7 in this color.

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So it's that side right
over there is of length 7.

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So it'll be 7 plus
this length over here,

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which is going to be 5.

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They tell us that.

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BC is 5.

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Plus 5.

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Plus DC is going to
be the same length

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is AB, which is
going to be 7 again.

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So plus 7.

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And then finally, DA a or AD,
however you want to call it,

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is going to be the same length
as BC, which is 5 again.

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So plus 5 again.

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So you have 7 plus 5 is 12
plus 7 plus 5 is 12 again.

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So you're going to
have a perimeter of 24.

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And you could go the
other way around.

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Let's say that you
have a square, which

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is a special case
of a rectangle.

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A square has 4 sides and 4 right
angles, and all of the sides

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are equal.

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So let me draw a square here.

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My best attempt.

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So this is A, B, C, D. And
we're going to tell ourselves

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that this right
here is a square.

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And let's say that this
square has a perimeter.

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So square has a perimeter of 36.

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So given that, what is the
length of each of the sides?

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Well, all the sides are going
to have the same length.

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Let's call them x.

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If AB is x, then BC is x,
then DC is x, and AD is x.

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All of the sides are congruent.

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All of these segments
are congruent.

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They all have the same
measure, and we call that x.

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So if we want to figure
out the perimeter here,

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it'll just be x plus x
plus x plus x, or 4x.

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Let me write that. x
plus x plus x plus x,

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which is equal to 4x, which
is going to be equal to 36.

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They gave us that
in the problem.

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And to solve this, 4
times something is 36,

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you could solve that
probably in your head.

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But we could divide
both sides by 4,

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and you get x is equal to 9.

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So this is a 9 by 9 square.

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This width is 9.

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This is 9, and then the height
right over here is also 9.

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So that is perimeter.

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Area is kind of a
measure of how much space

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does this thing take
up in two dimensions?

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And one way to think about area
is if I have a 1-by-1 square,

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so this is a 1-by-1 square--
and when I say 1-by-1,

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it means you only have
to specify two dimensions

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for a square or a rectangle
because the other two are

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going to be the same.

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So for example, you could
call this a 5 by 7 rectangle

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because that immediately
tells you, OK, this side is 5

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and that side is 5.

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This side is 7,
and that side is 7.

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And for a square, you could
say it's a 1-by-1 square

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because that specifies
all of the sides.

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You could really say,
for a square, a square

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where on one side is 1,
then really all the sides

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are going to be 1.

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So this is a 1-by-1 square.

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And so you can view
the area of any figure

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as how many 1-by-1 squares
can you fit on that figure?

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So for example, if we were going
back to this rectangle right

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here, and I wanted to find out
the area of this rectangle--

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and the notation
we can use for area

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is put something in brackets.

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So the area of rectangle
ABCD is equal to the number

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of 1-by-1 squares we can
fit on this rectangle.

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So let's try to do
that just manually.

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I think you already
might get a sense of how

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to do it a little bit quicker.

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But let's put a bunch of 1-by-1.

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So let's see.

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We have 5 1-by-1 squares
this way and 7 this way.

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So I'm going to try my
best to draw it neatly.

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So that's 1, 3, 3,
4, 5, 6, and then 7.

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1, 2, 3, 4, 5, 6, 7.

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So going along one of the
sides, if we just go along

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one of the sides like
this, you could put 7 just

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along one side just like that.

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And then over here,
how many can we see?

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We see that's 1 row.

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And that's 2 rows.

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Then we have 3 rows and
then 4 rows and then 5 rows.

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1, 2, 3, 4, 5.

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And that makes sense because
this is 1, 1, 1, 1, 1.

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Should add up to 5.

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These are 1, 1, 1, 1, 1, 1, 1.

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Should add up to 7.

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Yup, there's 7.

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So this is 5 by 7.

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And then you could
actually count these,

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and this is kind of straight
forward multiplication.

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If you want to know the
total number of cubes here,

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you could count it, or you can
say, well, I've got 5 rows,

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7 columns.

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I'm going to have 35--
did I say cube-- squares.

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I have 5 squares in this
direction, 7 in this direction.

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So I'm going to have
35 total squares.

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So the area of this figure
right over here is 35.

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And so the general
method, you could just

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say, well, I'm just going to
take one of the dimensions

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and multiply it by
the other dimension.

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So if I have a
rectangle, let's say

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the rectangle is
1/2 by 1/2 by 2.

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Those are its dimensions.

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Well, you could
just multiply it.

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You say 1/2 times 2.

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The area here is going to be 1.

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And you might say, well,
what does 1/2 mean?

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Well, it means,
in this dimension,

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I could only fit 1/2
of a 1-by-1 square.

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So if I wanted to do
the whole 1-by-1 square,

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it's all distorted here.

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It would look like that.

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So I'm only doing half of one.

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I'm doing another half
of one just like that.

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And so when you add this
guy and this guy together,

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you are going to
get a whole one.

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Now what about area of a square?

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Well, a square is
just a special case

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where the length and
the width are the same.

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So if I have a square--
let me draw a square here.

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And let's call that XYZ-- I
don't know, let's make this S.

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And let's say I wanted
to find the area

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and let's say I know
one side over here is 2.

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So XS is equal to 2, and I
want to find the area of XYZS.

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So once again, I
use the brackets

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to specify the area of this
figure, of this polygon right

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here, this square.

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And we know it's a square.

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We know all the sides are equal.

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Well, it's a special
case of a rectangle where

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we would multiply the
length times the width.

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We know that they're
the same thing.

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If this is 2, then
this is going to be 2.

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So you just multiply 2 times 2.

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Or if you want to
think of it, you

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square it, which is
where the word comes

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from-- squaring something.

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So you multiply 2 times 2,
which is equal to 2 squared.

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That's where the
word comes from,

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finding the area of a
square, which is equal to 4.

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And you could see
that you could easily

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fit 4 1-by-1 squares
on this 2-by-2 square.

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