Decomposing shapes to find area (add) | Math | 3rd grade | Khan Academy

- [Voiceover] What is
the area of the figure?

So down here we have this one, two, three,

four, five, six, seven,
eight, nine, 10-sided figure,

and we want to know its area,

how many square meters
does this figure cover?

And we have some measurements,

that seems helpful,

but what's not too helpful to me is

I don't know the special trick

to find the area of a 10-sided figure

so I've got to think about what I do know

and what I do know

is the way to find area of a rectangle.

So what I can do, because I can see,

if I can find any rectangles in here.

Here's one rectangle, right there.

So I can find the area of that part.

Then let's see if I can find any more.

Here's another rectangle.

So I can find the area of that part.

We could call that one
a rectangle or a square.

And then that leaves
us with this last part,

which is again, a rectangle.

So what we did is, we broke this up

or decomposed it into three rectangles

and now if I find out how much space

this purple one covers,

and the blue one and the green one,

if I combine those, that
would tell me the area

of the entire figure,

how much space the entire figure covers.

So let's start with this one right here.

This one is three meters long,

so we can kind of divide
that by three meters,

into three equal meters,

and then we've got a width
of two meters down here

so we can split that in half.

So if we draw those lines out,

we can see this top row is
going to cover one square meter,

two square meters, three square meters,

and then there's two rows of that,

so there's two rows

of three square meters

for a total of six square meters.

This rectangle covers six square meters,

so this part of the entire figure

covers six square meters.

The next one, our measurements
are three and a three,

so it will have three rows
of three square meters

or nine square meters,

and then finally this purple one

has three meters and nine,

so we can say it will
have three rows of nine

or nine rows of three square meters

which is 27 square meters.

So the area

of this purple section,

it covers completely 27 square meters.

The green covers nine square meters,

and the blue covered six square meters.

So, if we combine all those areas,

all those square meters it covers,

that will tell us the
area of the entire figure.

So we have six square meters,

plus nine square meters,

plus 27,

and we can solve that,
six plus nine is 15,

15 plus 27, let's see,

five ones and seven ones

is 12 ones.

We'll just find some space up there.

And

one 10 and two 10's

or a 10 and a 20

is 30.

And 30 plus 12 is 42.

So the area of the entire figure is

42

square

meters.