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## Geometry (all content)

### Course: Geometry (all content) > Unit 6

Lesson 5: Quadrilaterals on the coordinate plane- Coordinates of a missing vertex
- Area of a parallelogram on the coordinate plane
- Area and perimeter on the coordinate plane
- Dimensions of a rectangle from coordinates
- Coordinates of rectangle example
- Quadrilateral problems on the coordinate plane
- Quadrilateral problems on the coordinate plane

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# Area of a parallelogram on the coordinate plane

CCSS.Math:

Learn how to find the area of a parallelogram on the coordinate plane.

## Want to join the conversation?

- This is a great video; everything is explained very well, but the exercise does not have visual aid like how this is taught. That would be okay if it was explained how to solve without a visual grid, but it wasn't. Sal, could you please give an additional explanation on how to do this in your head? It's a bit confusing without it.

Much appreciated! :)

**Please, vote up! Please don't misunderstand me and flag this, because it's not for me, but so that we can keep it emphasized and get this explained!*(64 votes) - I'm so confused. The question doesn't let us do this(13 votes)
- Hey Dylan! I recommend choosing the exercise "Drawing polygons on the coordinate plane". There, you will see the coordinate plane. Place the coordinates, and solve! (
**do not press check, you are just clicking on that exercise for the plane**)(10 votes)

- no fair you get all these colors and tools and we don't(9 votes)
- Sal uses software that has tools he uses in his videos. You can also download the software if you wish. SmoothDraw3(10 votes)

- With the height, how is it 4? there was one square that was 1/2. shouldn't it be 3/2?(5 votes)
- Good question! Imagine taking the bottom triangular part of the parallelogram (like you cut it off) and moving it up, so you make a rectangle. Now you can see that the height is 4, and the area of a rectangle is just base * height.(4 votes)

- What about perimeter not area?(8 votes)
- how do we do things like that without having the shape in front of us do we just guess(6 votes)
- it doesn't help me :((5 votes)
- Hi Ashley! I say use the coordinate planes provided in the exercise before. After placing the line segments, count the side measurements and multiply them. For example, polygon A = __ square units(2 votes)

- I don't understand this(5 votes)
- Aren't we supposed to divide the area of each of the two triangles by two and add those to the area of the parallelogram?(3 votes)
- ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠈⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⣄⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⢀⠀⢀⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣉⣩⣤⠴⠶⠶⠒⠛⠛⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠤⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀

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⠀⢠⣿⠋⠻⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠛⢦⣽⣿⣿⢻⣿⣿⣿⣿⠋⠁⠘⣿⣿⣿⣿⣿⣿⣼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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## Video transcript

- [Voiceover] Let's see if we can find the area of this parallelogram, and I encourage you to pause the video and see if you can figure
it out on your own. Well, we just have to remind ourselves that the area of a parallelogram is just going to be the base -- let me do this in different colors -- it's going to be the base
of the parallelogram, so I want to do that in a different color, so let me write: the base of the parallelogram times the height of the parallelogram, times the height of the parallelogram. Area is equal to base times height. So, what could we consider to be the base of this parallelogram? Well, we could imagine it
to be one of these sides. So, we could go from here, and so, I could say... well, I could consider
this to be the base. So, what's the length of that base? Well, we're just going in
the vertical direction. We go from "y" equals five, to "y" is equal to negative seven, so this has length 12. We have five above the x-axis,
and seven below the x-axis, adding up to 12. Or, you could count it: One, two, three, four, five, six, seven, eight, nine, ten, 11, 12. So, this is our base, and we could say that base is equal to 12. And, now, what could
we view as our height? Well, we could view this dimension, right over here, as our height. And, what is that going to be? Well, you can see very clearly that the height is equal to four. And, it might be a
little counter-intuitive, 'cause normally, when
you're talking about height, you're used to thinking
about how high something is, but you could imagine rotating this around so that the base is laying flat, and then the height is the height, in the traditional sense of the word. But, we could say "h" is equal to four, and now, it's pretty straightforward. Our area is going to be equal to 12, the length of our base times our height, times four, times four, which is clearly just 48. 48, whatever, square, 48 square units.