Area of a parallelogram

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 I 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 move diagonally we're talking about if you go from that's from from this side up here and you were to go straight down if you were to go at a 90-degree angle if you would 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 based on its height what do we think its area is going to be so at first it might seem well you know this isn't 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 copy let me do it a little bit better so this 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 gonna move this section of area remember we're just talking about how much 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 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 move 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 because 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 looking more like a parallelogram again the area of a parallelogram is just going to be if you have the base of 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