Main content

## Geometry 218-221

# Finding area by rearranging parts

CCSS.Math:

Sometimes it helps to rearrange the parts of geometric figures to find the area. That's what we're going to do here. Created by Sal Khan.

## Want to join the conversation?

- i dont understand any of this(34 votes)
- What don't you understand? If its why moving the shape works, then its because the area of the shape is only being shifted to another side of the object. This still counts as part of the area even though its shifted. The reason why you shift part of the are to another side is so that its easier to calculate.(3 votes)

- I have math homework that is about finding the area of a polygon, could you make a video on that please ?

thank you(6 votes)- Finding the area of a polygon is quite simple. I'll explain how to do so here. Let's say we have a hexagon. Each side of the hexagon is 7 inches. The first step is to divide the hexagon into triangles and find one of their areas. Say the triangle had a base of 7in and a height of 4in. Figure out the area (which would be 14 sq in.) Now, multiply 14 by the amount of sides that the shape has. So 14x6, which is 84. Therefore, the area of the polygon is 84 square inches.

I hope this helped!(9 votes)

- i am so confused i know what to do but at the same time i do not how to have a shape that does not already have the base and height for me(7 votes)
- what im still confused i dont understand anything.(2 votes)
- well, they are showing how these different quadrilateral's area is being found. The green one can either be like blue(if you remove the extra triangles) or the red(if you finish the triangle by bringing up or down one.) and for the pink we have an extra that cant be finished, so it is left, and if you compare green and pink pink is bigger with the extra.

hope it is useful!(3 votes)

- can someone please help me? so my problem is,

'Liza and Abby plan to spread out blankets at a park for a picnic with some friends. The park is crowded, so they end up overlapping the blankets as is shown in the diagram.'

the top blanket is,

top: 5.7

left side: 5

bottom: 4

the side blanket is making the side of the other one make the corner a triangle and it forms a triangle that way.

and the bottom of the triangle is 5.7

the rectangle is

left side; 6

right side; 2

bottom; 4(4 votes) - i dont understand any of this

*(4 votes) - what is he talking about?(4 votes)
- why aren't math no easy?(3 votes)
- How can I find the length and width of a figure knowing the area(2 votes)
- Find the factors of the area. The factors are the length and width.(2 votes)

- With the pink one, why did he not count the 'extra'?(2 votes)
- Sal was desperately in search for the one similar to the green quadrilateral . So , after finding out that the green one had extra right angled triangle , he skipped that and went forward . Hope that helped.(2 votes)

## Video transcript

We have four quadrilaterals
drawn right over here. And what I want
us to think about is looking at this green
quadrilateral here. I want you to pause
the video and think about which of
these figures have the same area as the
green quadrilateral? And so pause the video
now and think about that. So I'm assuming you
gave a shot at it. Now let's think about it. And the way I'm
going to think about is to really rearrange parts
of this green quadrilateral to make it look
more like maybe some of these other quadrilaterals. So for example, if
we were to if we were to put a little
dotted line right over here and a dotted line
right over here, we see that our green
shape is actually made up, you could imagine it being made
up of, a triangle, and then a rectangle, and then
another triangle. And what's interesting
about the two triangles is that they represent
the exact same area. They essentially
both represent, they each represent half of this
rectangle right over here. Let me do that in a color. They represent half
of this entire thing if I were to color it all in. And if you have
trouble visualizing it, imagine taking this top
part right over here and then flipping it over. It would look like this. If you flip it over, this
line right over here, it would look
something like this. My best attempt to draw it. So take that top section, it
would look something like that. And then move it down right
over here to fit in here. And then this plus this will
fill in this entire region right over here. So that original green trapezoid
that we were looking at, if you take that top
part out, it essentially has the exact same area
as a rectangle that has a height of 4
and a length of 5. So this right over here
has the exact same area as our trapezoid. And once again,
how did we do that? Well, we just took
this top part, flipped it over, and
relocated it down here. And we said hey,
we could actually construct a rectangle that way. So essentially, and if
you want to know its area, we could either just
count the squares here. So we have, let me do
this in an easier to see. So we have 1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 of these
unit squares right over here. And we know that there's
an easier way to do that. We could have just multiplied
the height times the width. We could have just said,
look this thing is 1, 2, 3, 4 high and 1, 2, 3, 4, 5 wide. So 4 times 5 is going to give
us 20 of these units squares. So that's the area in terms of
unit squares, or square units, of that original
green trapezoid. Now let's see which one
of these match that. So this pink one
right over here. If you don't even
count this bottom part, if you were to just separate
this top part right over here. This top part is
4 high by 5 wide. So just this top
part alone is 20. And then it has this
extra right over here. So the pink has a
larger area than our original green trapezoid. The blue rectangle is 3 by 5. So it has an area
of 15 square units. Now the red one is interesting. It is 1, 2, 3, 4 high and 1,
2, 3, 4, 5 long or 5 wide. 4 times 5 is 20 squares,
and you can validate that. And so the red rectangle
has the same area as our original green trapezoid.