Area of a kite

What is the area of this figure?

And this figure right
over here is sometimes

called a kite for
obvious reasons.

If you tied some
string here, you

might want to fly
it at the beach.

And another way to think
about what a kite is,

it's a quadrilateral that is
symmetric around a diagonal.

So this right over here is the
diagonal of this quadrilateral.

And it's symmetric around it.

This top part and this bottom
part are mirror images.

And to think about how we
might find the area of it

given that we've been
given essentially

the width of this
kite, and we've also

been given the
height of this kite,

or if you view this
as a sideways kite,

you could view this
is the height and that

the eight centimeters
as the width.

Given that we've got
those dimensions,

how can we actually
figure out its area?

So to do that, let
me actually copy

and paste half of the kite.

So this is the bottom
half of the kite.

And then let's take the
top half of the kite

and split it up into sections.

So I have this little
red section here.

I have this red section here.

And actually, I'm going to try
to color the actual lines here

so that we can keep
track of those as well.

So I'll make this line green
and I'll make this line purple.

So imagine taking this little
triangle right over here--

and actually, let me do
this one too in blue.

So this one over here is blue.

You get the picture.

Let me try to color it
in at least reasonably.

So I'll color it in.

And then I could make this
segment right over here,

I'm going to make orange.

So let's start focusing
on this red triangle here.

Imagine flipping it over and
then moving it down here.

So what would it look like?

Well then the green side is
going to now be over here.

This kind of mauve colored
side is still on the bottom.

And my red triangle is going
to look something like this.

My red triangle is
going to look like that.

Now let's do the same thing
with this bigger blue triangle.

Let's flip it over and
then move it down here.

So this green side, since we've
flipped it, is now over here.

And this orange side
is now over here.

And we have this
blue right over here.

And the reason that we know
that it definitely fits

is the fact that it is
symmetric around this diagonal,

that this length
right over here is

equivalent to this
length right over here.

That's why it fits
perfectly like this.

Now, what we just
constructed is clearly

a rectangle, a rectangle that
is 14 centimeters wide and not

8 centimeters high, it's
half of 8 centimeters high.

So it's 8 centimeters times
1/2 or 4 centimeters high.

And we know how to
find the area of this.

This is 4 centimeters
times 14 centimeters.

So the area is equal
to 4 centimeters

times 14 centimeters which
is equal to-- let's see,

that's 40 plus 16--
56 square centimeters.

So if you're taking
the area of a kite,

you're really just
taking 1/2 the width

times the height, or 1/2
the width times the height,

any way you want
to think about it.