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6th grade

Course: 6th gradeย >ย Unit 8

Lesson 1: Areas of parallelograms
Math
6th grade
Plane figures
Areas of parallelograms
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Area of a parallelogram

CCSS.Math:
6.G.A.1
Google Classroom
Understand why the formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

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  • marcimus purple style avatar for user Ala Mokhtabad
    Posted 6 years ago. Direct link to Ala Mokhtabad's post โ€œI have two questions: 1. ...โ€
    I have two questions:
    1. Does this work for all quadrilaterals?
    2. Why is there a 90 degree in the parallelogram?
    (89 votes)
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    • winston default style avatar for user Joel
      Posted 6 years ago. Direct link to Joel's post โ€œ1. No, this only works fo...โ€
      Incredible Answer
      Great Answer
      Good Answer
      1. No, this only works for parallelograms
      2. A parallelogram is defined as a shape with 2 sets of parallel sides, so this means that rectangles are parallelograms. By definition rectangles have 90 degree angles, but if you're talking about a non-rectangular parallelogram having a 90 degree angle inside the shape, that is so we know the height from the bottom to the top. It has to be 90 degrees because it is the shortest length possible between two parallel lines, so if it wasn't 90 degrees it wouldn't be an accurate height.
      (100 votes)
  • aqualine ultimate style avatar for user _:*.Big_Star_Wars_Fan.*:_
    Posted 3 years ago. Direct link to _:*.Big_Star_Wars_Fan.*:_'s post โ€œI have 3 questions: 1. D...โ€
    I have 3 questions:

    1. Dose it mater if u put it like this: A= b x h or do you switch it around?

    2. Will it work for circles?

    3. How many different kinds of parallelograms does it work for?

    And may I have a upvote because I have not been getting any.
    (68 votes)
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    • blobby green style avatar for user Alatheia Hague
      Posted 3 years ago. Direct link to Alatheia Hague's post โ€œIt doesn't matter if u sw...โ€
      It doesn't matter if u switch bxh around, because its just multiplying. When you multiply 5x7 you get 35. If you multiply 7x5 what do you get? You get the same answer, 35.

      2.There is a diffrent formula for a circle, triangle, cimi circle, it goes on and on. The formula for circle is:
      A= Pi x R squared.
      (8 votes)
  • hopper cool style avatar for user James Wetzel
    Posted a month ago. Direct link to James Wetzel's post โ€œIf you upvote my stuff, I...โ€
    If you upvote my stuff, I will upvote yours.
    (13 votes)
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  • starky ultimate style avatar for user Pablo Lopez
    Posted 3 years ago. Direct link to Pablo Lopez's post โ€œWhat is the formula for a...โ€
    What is the formula for a solid shape like cubes and pyramids?
    (7 votes)
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    • primosaur seed style avatar for user Ian Pulizzotto
      Posted 3 years ago. Direct link to Ian Pulizzotto's post โ€œNice question! For 3-D s...โ€
      Good Answer
      Nice question!

      For 3-D solids, the amount of space inside is called the volume. Volume in 3-D is therefore analogous to area in 2-D.

      The volume of a cube is the edge length, taken to the third power. The volume of a rectangular solid (box) is length times width times height. Note that these are natural extensions of the square and rectangle area formulas, but with three numbers, instead of two numbers, multiplied together.

      The volume of a pyramid is one-third times the area of the base times the height. Note that this is similar to the area of a triangle, except that 1/2 is replaced by 1/3, and the length of the base is replaced by the area of the base.
      (10 votes)
  • old spice man green style avatar for user christopherj.mca
    Posted 23 days ago. Direct link to christopherj.mca's post โ€œUP VOTE IF YOU DON"T LIKE...โ€
    UP VOTE IF YOU DON"T LIKE THIS, AND COMMENT TO SUPPORT. To see the post yourself scroll down until you see nj421822 say "i think you're black." This was very disturbing for me to see this as a black child. I felt hurt and attacked until i saw that other kids stood up for black kids.

    Special Thanks to: Zach, Molly๐Ÿ“š, and beckler_a
    I thank y'all for the support.


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    nj421822
    19 days ago
    Posted 19 days ago. Direct link to nj421822's post โ€œI think your blackโ€
    I think your black
    Answer nj421822's post โ€œI think your blackโ€
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    Comment on nj421822's post โ€œI think your blackโ€
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    Zach
    10 days ago
    Posted 10 days ago. Direct link to Zach's post โ€œshut the hell upโ€
    shut the hell up

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    Molly๐Ÿ“š
    5 days ago
    Posted 5 days ago. Direct link to Molly๐Ÿ“š's post โ€œi agree with with @Zach. ...โ€
    i agree with with @Zach. thas wrong man

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    Posted 2 days ago. Direct link to beckler_a's post โ€œracisitโ€
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    christopherj.mca
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    Posted a few seconds ago. Direct link to christopherj.mca's post โ€œU r right i'm black and t...โ€
    U r right i'm black and this hurt my feelings. well if u think i'm black then i think u r racist and i say that for everyone who thought this was wrong, especially for all the black kids reading this.

    Comment on christopherj.mca's post โ€œU r right i'm black and t...โ€
    (1 vote)




    UP VOTE IF YOU DON"T LIKE THIS, AND COMMENT TO SUPPORT. To see the post yourself scroll down until you see nj421822 say "i think you're black." This was very disturbing for me to see this as a black child. I felt hurt and attacked until i saw that other kids stood up for us black kids.

    Special Thanks to: Zach, Molly๐Ÿ“š, and beckler_a
    I thank y'all for the support.
    (6 votes)
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  • blobby green style avatar for user 28nettlra
    Posted a month ago. Direct link to 28nettlra's post โ€œHonestly what are we doin...โ€
    Honestly what are we doin here dawg you all are math teachers that get paid half a block of McDonalds cheese teaching ungrateful kids for nothing just quit and become a millionaire
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    • leafers sapling style avatar for user Tulsi
      Posted 13 days ago. Direct link to Tulsi's post โ€œโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘...โ€
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–Œโ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘ this is doge
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–โ–„โ–€โ–’โ–’โ–€โ–€โ–€โ–€โ–„โ–„โ–„โ–€โ–’โ–’โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–„โ–€โ–’โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–ˆโ–’โ–’โ–„โ–ˆโ–’โ–โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–€โ–ˆโ–ˆโ–€โ–’โ–Œโ–‘โ–‘โ–‘
      โ–‘โ–‘โ–โ–’โ–’โ–’โ–„โ–„โ–’โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–„โ–’โ–’โ–Œโ–‘โ–‘ copy and paste him to take
      โ–‘โ–‘โ–Œโ–‘โ–‘โ–Œโ–ˆโ–€โ–’โ–’โ–’โ–’โ–’โ–„โ–€โ–ˆโ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–ˆโ–’โ–โ–‘โ–‘ khan academy
      โ–‘โ–โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–Œโ–ˆโ–ˆโ–€โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–€โ–„โ–Œโ–‘
      โ–‘โ–Œโ–‘โ–’โ–„โ–ˆโ–ˆโ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–Œโ–‘
      โ–โ–’โ–€โ–โ–„โ–ˆโ–„โ–ˆโ–Œโ–„โ–‘โ–€โ–’โ–’โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–โ–‘
      โ–โ–’โ–’โ–โ–€โ–โ–€โ–’โ–‘โ–„โ–„โ–’โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–’โ–’โ–Œ
      โ–โ–’โ–’โ–’โ–€โ–€โ–„โ–„โ–’โ–’โ–’โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–โ–‘
      โ–‘โ–Œโ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–€โ–€โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–’โ–Œโ–‘
      โ–‘โ–โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–„โ–’โ–’โ–โ–‘โ–‘
      โ–‘โ–‘โ–€โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–„โ–’โ–’โ–’โ–’โ–Œโ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–€โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–„โ–„โ–„โ–€โ–’โ–’โ–’โ–’โ–„โ–€โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–€โ–„โ–„โ–„โ–„โ–„โ–„โ–€โ–€โ–€โ–’โ–’โ–’โ–’โ–’โ–„โ–„โ–€โ–‘โ–‘โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–€โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘ and the world :>
      (2 votes)
  • blobby green style avatar for user Annie Ma
    Posted 2 years ago. Direct link to Annie Ma's post โ€œ1. Does it work on a quad...โ€
    1. Does it work on a quadrilaterals?
    2. Can this also be used for a circle?
    Sorry for so my useless questions :(
    (4 votes)
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  • starky seedling style avatar for user pasangs23
    Posted 25 days ago. Direct link to pasangs23's post โ€œI swear they say MaTh Is ...โ€
    I swear they say MaTh Is FuN more LikE BoriNg
    (5 votes)
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    • leafers sapling style avatar for user Tulsi
      Posted 13 days ago. Direct link to Tulsi's post โ€œโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘...โ€
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–Œโ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘ this is doge
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–โ–„โ–€โ–’โ–’โ–€โ–€โ–€โ–€โ–„โ–„โ–„โ–€โ–’โ–’โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–„โ–€โ–’โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–ˆโ–’โ–’โ–„โ–ˆโ–’โ–โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–€โ–ˆโ–ˆโ–€โ–’โ–Œโ–‘โ–‘โ–‘
      โ–‘โ–‘โ–โ–’โ–’โ–’โ–„โ–„โ–’โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–„โ–’โ–’โ–Œโ–‘โ–‘ copy and paste him to take
      โ–‘โ–‘โ–Œโ–‘โ–‘โ–Œโ–ˆโ–€โ–’โ–’โ–’โ–’โ–’โ–„โ–€โ–ˆโ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–ˆโ–’โ–โ–‘โ–‘ khan academy
      โ–‘โ–โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–Œโ–ˆโ–ˆโ–€โ–’โ–’โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–€โ–„โ–Œโ–‘
      โ–‘โ–Œโ–‘โ–’โ–„โ–ˆโ–ˆโ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–Œโ–‘
      โ–โ–’โ–€โ–โ–„โ–ˆโ–„โ–ˆโ–Œโ–„โ–‘โ–€โ–’โ–’โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–โ–‘
      โ–โ–’โ–’โ–โ–€โ–โ–€โ–’โ–‘โ–„โ–„โ–’โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–’โ–’โ–Œ
      โ–โ–’โ–’โ–’โ–€โ–€โ–„โ–„โ–’โ–’โ–’โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–โ–‘
      โ–‘โ–Œโ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–€โ–€โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–’โ–Œโ–‘
      โ–‘โ–โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–’โ–„โ–’โ–’โ–โ–‘โ–‘
      โ–‘โ–‘โ–€โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–‘โ–’โ–‘โ–’โ–‘โ–’โ–„โ–’โ–’โ–’โ–’โ–Œโ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–€โ–„โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–„โ–„โ–„โ–€โ–’โ–’โ–’โ–’โ–„โ–€โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–€โ–„โ–„โ–„โ–„โ–„โ–„โ–€โ–€โ–€โ–’โ–’โ–’โ–’โ–’โ–„โ–„โ–€โ–‘โ–‘โ–‘โ–‘โ–‘
      โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–’โ–€โ–€โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘
      (2 votes)
  • piceratops ultimate style avatar for user Jonathan Cortez
    Posted a month ago. Direct link to Jonathan Cortez's post โ€œwhats the point of this s...โ€
    whats the point of this stuff? its not like were gonna use in in life and why does we always say "WhEn I Do ThIs YoUr GoNnA sEe SoMeThInG AmAzInG" like broits so annoying
    (4 votes)
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  • leafers sapling style avatar for user Tulsi
    Posted 13 days ago. Direct link to Tulsi's post โ€œโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘...โ€
    โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–‘โ–‘โ–‘โ–‘
    โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–Œโ–‘โ–‘โ–‘
    โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–Œโ–’โ–’โ–ˆโ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–„โ–€โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘ this is doge
    โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–โ–„โ–€โ–’โ–’โ–€โ–€โ–€โ–€โ–„โ–„โ–„โ–€โ–’โ–’โ–’โ–’โ–’โ–โ–‘โ–‘โ–‘
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    โ–โ–’โ–€โ–โ–„โ–ˆโ–„โ–ˆโ–Œโ–„โ–‘โ–€โ–’โ–’โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–‘โ–’โ–’โ–’โ–โ–‘
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Video transcript

- 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.