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## Geometry 218-221

# Area of a parallelogram

CCSS.Math:

Understand why the formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

## Want to join the conversation?

- 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.(53 votes)- 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)

- What is the formula for a solid shape like cubes and pyramids?(8 votes)
- That is a great question to ask us. 1st, you undo the net, then you multiply all of the square's, then you want to add them. Kra-BOOM! Genius!(2 votes)

- 1. Does it work on a quadrilaterals?

2. Can this also be used for a circle?

Sorry for so my useless questions :((7 votes)- The formula for quadrilaterals like rectangles

and parallelograms is always base times height.

The formula for a circle is pi to the radius squared.

Also these questions are not useless. :)(1 vote)

- What is the formula for a solid shape like cubes and pyramids(3 votes)
- In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base.(2 votes)

- What about parallelograms that are sheared to the point that the height line goes outside of the base? I can't manipulate the geometry like I can with the other ones. Would it still work in those instances?(3 votes)
- then how do we get the tip of the area(3 votes)
- This video was very helpful, thank you.(3 votes)
- How do you do quantum mechanics(3 votes)
- I have one question:

How do you calculate the angle degree of a dodecagon?(2 votes)- Use this formula..
*(side-2)*180*...So take the number of sides and subtract two and then multiply it by 180...This works for all polygons.

p.s. if you want to see how it works check out this..

https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-interior-angles-of-a-polygon(3 votes)

- How can you find area on 3-d shapes?(2 votes)
- Great question!

For 3-Dimensional shapes there is a formula called volume, and volume is basically when you multiply Length times width times height. So you would NOT say"How can you find the area of a 3-Dimensional figure" you would say"How can you find the VOLUME of a 3-Dimensional figure".But that's something you learn a bit later in 6th grade.(1 vote)

## 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.