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Area of a parallelogram on the coordinate plane

In math, we can find the area of a parallelogram by multiplying the base by the height. The base is one side, and the height is the distance from the base to the opposite side. So, if the base is 12 units and the height is 4 units, the area is 48 square units.

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Video transcript

- [Instructor] Let's see if we can find the area of this parallelogram. 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, which I wanna 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. And 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, 10, 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 this might be a little counterintuitive, 'cause normally when you're talking about height, you're used to thinking about how high something is. But you can imagine rotating this around so that this is laying, 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.