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## 6th grade

### 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?(90 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.(103 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.(70 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.(10 votes)

- What is the formula for a solid shape like cubes and pyramids?(8 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.(11 votes)

- 1. Does it work on a quadrilaterals?

2. Can this also be used for a circle?

Sorry for so my useless questions :((4 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. :)(5 votes)

- Great but doesn't answer my question. What are the properties of parallelogram?(5 votes)
- A parallelogram is defined as a quadrilateral with two pairs of parallel sides. This implies the following properties:

1. Pairs of opposite (parallel) sides are equal.

2. Pairs of opposite angles are equal.

3. Any two consecutive angles sharing a common side are supplementary (that is, they add to 180 degrees).

4. The two diagonals intersect at their common midpoint.

5. Each diagonal alone divides the parallelogram into two congruent triangles.

6. The two diagonals together divide the parallelogram into two pairs of congruent triangles.

Have a blessed, wonderful day!(5 votes)

- whats the point of this stuff? its not like were gonna use in in life and why does we always say "WhEn I Do ThIs YoUr GoNnA sEe SoMeThInG AmAzInG" like broits so annoying(6 votes)
- unless u want to be homeless u have to take the SAT which contains these stuff(3 votes)

- I thought to find area you use length x width to figure it out.(5 votes)
- Sal put base instead of width probably to make people understand more easly about Parallelogram (I have a hard time saying width)(4 votes)

- Me goofing around down here(5 votes)
- this is too easy(5 votes)

## 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.