Area of a Parallelogram Video Lecture - Class 7

- If we have a rectangle
with base length b
and height length h, we know
how to figure out its area.
Its area is just going to be the base,
is going to be the base times the height.
The base times the height.
This is just a review of
the area of a rectangle.
Just multiply the base times the height.
Now let's look at a parallelogram.
And in this parallelogram,
our base still has length b.
And we still have a height h.
So when we talk about the height,
we're not talking about the
length of these sides that
at least the way I've drawn
them, move diagonally.
We're talking about if you
go from this side up here,
and you were to go straight down.
If you were to go at a 90 degree angle.
If you were to go
perpendicularly straight down,
you get to this side, that's going to be,
that's going to be our height.
So in a situation like this
when you have a parallelogram,
you know its base and its height,
what do we think its area is going to be?
So at first it might seem
well this isn't as obvious
as if we're dealing with a rectangle.
But we can do a little visualization
that I think will help.
So what I'm going to do is I'm
going to take a chunk of area
from the left-hand side,
actually this triangle
on the left-hand side that
helps make up the parallelogram,
and then move it to the right,
and then we will see
something somewhat amazing.
So I'm going to take this,
I'm going to take this
little chunk right there,
Actually let me do it a little bit better.
So I'm going to take
that chunk right there.
And let me cut, and paste it.
So it's still the same parallelogram,
but I'm just going to
move this section of area.
Remember we're just thinking about
how much space is inside
of the parallelogram
and I'm going to take
this area right over here
and I'm going to move it
to the right-hand side.
And what just happened?
What just happened?
Let me see if I can move
it a little bit better.
What just happened when I did that?
Well notice it now looks just
like my previous rectangle.
That just by taking some of the area,
by taking some of the area from the left
and moving it to the right,
I have reconstructed this rectangle
so they actually have the same area.
The area of this parallelogram,
or well it used to be this parallelogram,
before I moved that triangle
from the left to the right,
is also going to be the
base times the height.
So the area here is also the area here,
is also base times height.
I just took this chunk of
area that was over there,
and I moved it to the right.
So the area of a parallelogram,
let me make this looking more
like a parallelogram again.
The area of a parallelogram
is just going to be, if you
have the base and the height,
it's just going to be the
base times the height.
So the area for both of these,
the area for both of these,
are just base times height.