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### Course: 6th grade > Unit 8

Lesson 1: Areas of parallelograms# 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!

## Want to join the conversation?

- I have two questions:

1. Does this work for all quadrilaterals?

2. Why is there a 90 degree in the parallelogram?(101 votes)- 1. No, this only works for parallelograms

2. A parallelogram is defined as a shape with 2 sets of parallel sides, so this means that rectangles are parallelograms. By definition rectangles have 90 degree angles, but if you're talking about a non-rectangular parallelogram having a 90 degree angle inside the shape, that is so we know the height from the bottom to the top. It has to be 90 degrees because it is the shortest length possible between two parallel lines, so if it wasn't 90 degrees it wouldn't be an accurate height.(122 votes)

- 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.(92 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.(15 votes)

- What is the formula for a solid shape like cubes and pyramids?(4 votes)
- Nice question!

For 3-D solids, the amount of space inside is called the volume. Volume in 3-D is therefore analogous to area in 2-D.

The volume of a cube is the edge length, taken to the third power. The volume of a rectangular solid (box) is length times width times height. Note that these are natural extensions of the square and rectangle area formulas, but with three numbers, instead of two numbers, multiplied together.

The volume of a pyramid is one-third times the area of the base times the height. Note that this is similar to the area of a triangle, except that 1/2 is replaced by 1/3, and the length of the base is replaced by the area of the base.(9 votes)

- I still don't really get it.(5 votes)
- To find the area of a parallelogram, you need the length of a base and the length of the height.

Area = base * height(2 votes)

- 1. Does it work on a quadrilaterals?

2. Can this also be used for a circle?

Sorry for so my useless questions :((3 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. :)(4 votes)

- i don't understand is a parallelogram many shapes or just one ?(3 votes)
- but how do you calculate the base and or height using this?(3 votes)
- If you know the area of the parallelogram and only
`1`

of either base or height, you can find the other by dividing area by that.

Examples:

Area`32`

and height`8`

=> base`32/8 = 4`

Area`27`

and base`3`

=> height`27/3 = 9`

It's basically working backwards from the Area formula.

Hope this helped!(2 votes)

- i do not get it :(. help me please(3 votes)
- Hey if you give me something a bit more specific I can walk you through it :)(2 votes)

- I still do not get it. after watching it 10 times!(3 votes)
- Why can‘t the area of the parallelogram be the base*diagonal, if you pull it straight,I think it is still going to be the same area?(3 votes)
- Nah, we can't pull it like that, as it is more arbritrary and it can easily warp the shape and make it have a different area.

Something like slicing/rearranging the shape is more concrete. This is how we can rearrange all parallelograms into a rectangle with the same base and height as length and width :)(2 votes)

## 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.