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Finding area by rearranging parts

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.

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  • leaf blue style avatar for user eleblanc26
    i dont understand any of this
    (34 votes)
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    • duskpin ultimate style avatar for user Elaina163
      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)
  • duskpin ultimate style avatar for user Reagan
    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)
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    • male robot johnny style avatar for user Lila Piper
      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!
      (10 votes)
  • aqualine ultimate style avatar for user erin husky🐺
    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)
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  • blobby blue style avatar for user Elizabeth
    what im still confused i dont understand anything.
    (2 votes)
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    • sneak peak blue style avatar for user SmashedMonster
      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)
  • female robot grace style avatar for user Isabella sandoval
    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)
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  • aqualine ultimate style avatar for user Kristen
    i dont understand any of this
    *
    (4 votes)
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  • starky sapling style avatar for user chickenchip
    what is he talking about?
    (4 votes)
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  • ohnoes default style avatar for user TheBubblegumShark
    why aren't math no easy?
    (3 votes)
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  • blobby green style avatar for user Cynthia
    How can I find the length and width of a figure knowing the area
    (2 votes)
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  • starky ultimate style avatar for user Jai Harrison
    With the pink one, why did he not count the 'extra'?
    (2 votes)
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    • aqualine tree style avatar for user Jůp
      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.