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Area of a parallelogram

Discover the magic of geometry! The area of a rectangle and a parallelogram can be calculated in the same way. Just multiply the base by the height! This simple trick works because a parallelogram can be rearranged into a rectangle. Geometry is full of surprises!

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Video transcript

- [Narrator] If we have a rectangle with base length h 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. You 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, moved diagonally. We're talking about if you go from, that's 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 it's base and its height, what do we think its area is going to be? So at first, it might seem, well, you know, 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 gonna 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 gonna take this, I'm gonna take this little chunk right there. Actually, let me copy it, let me do it a little bit better. So this, I'm gonna take that chunk right there and let me cut and paste it, so it's still the same parallelogram, but I'm just gonna move this section of area. Remember we're just thinking about how much, how much is space is inside of the parallelogram. And I'm gonna take this area right over here and I'm gonna 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 on 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 what used to be the 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. 'Cause once again, I just took this chunk of area that was over there and I moved it to the right. So the area of a parallelogram, the area, let me make this look even 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.