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### Course: Geometry (Eureka Math/EngageNY) > Unit 3

Lesson 1: Topic A: Area- Intro to area and unit squares
- Compare area with unit squares
- Area of composite shapes
- Perimeter & area of composite shapes
- Area of composite shapes
- Scale factors and area
- Solving a scale drawing word problem
- Relate scale drawings to area
- Area of a circle intuition

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# Intro to area and unit squares

Together, we'll explore a video introducing area by comparing two figures' space on a surface. Using unit squares, we'll measure their areas, emphasizing the importance of a unit square for measuring various shapes. Created by Sal Khan.

## Want to join the conversation?

- How does area help the real world?(75 votes)
- Area is used for many things. Here are a few...

1) How large is the plot of land that I own?

2) How large is my house or apartment?

3) I want to paint a room. How much paint I need to buy is based upon the area of the walls of my room..

4) I wand to carpet a floor. Carpeting and other types of flooring are sold by the square foot, which is a measurement of area. So, I need to calculate the area of my room to find out how much carpet to buy.(81 votes)

- Is the unit square have to have the lengths so it could be a unit square or can it be a unit square with different lengths Also can we use shapes that are different for example: a rectangle?

Thank you <3(10 votes)- A square can have any side length as long as all the sides have the same length. For a square to be a unit square, its sides must be 1 unit long. If a square has side lengths that are not equal to 1, it cannot be called a unit square. Sure! You can use other shapes as long if they will make your work easier. For example, in the above video, if we used a 2 by 1 rectangle to measure, we would be able to put 2.5 rectangles in the blue figure and 5 rectangles in the purple figure.(15 votes)

- how do find the area of a triangle?(5 votes)
- The formula:
`A = (b * h) / 2`

The area is the base times the height, divided by 2.

So, if we had a triangle with a base of 2 and a height of 10, we would do.`A = (2 * 10) / 2 = 20 / 2 = 10`

Area is 10.(21 votes)

- how we measure the units squares correctly?(8 votes)
- Unit squares are representative of any square unit and take the place of any distance unit squared, like feet squared, meters squared, inches squared, and centimeters squared.(8 votes)

- do we have to really use the unit squares to measure it?(6 votes)
- You use unit squares when you don't have a measuring unit. They are mainly used when you are introduced to area, etc. They are not used in real-life circumstances but they are the foundations of the area, etc.

I hope it helps.(8 votes)

- How do you find the area of a pentagon?(6 votes)
- You can divide it into 5 triangles.

If it is a regular pentagon, which means all its sides are the same length, you can just draw two lines from the vertices to the center and then measure the base and height of this triangle. The area of the triangle is given by base*height/2 and you have 5 of these triangles in the pentagon so you multiply by 5.

For example if the side lengths of the pentagon are 5, and the distance between a midpoint of the sides and the center is 4. Then the area is 5*5*4/2 = 50

If the pentagon is not regular you have to split it into 5 triangles and measure each one(5 votes)

- So if a unit^2 is cubed, and a unit^3 is squared, then what do we call a unit^4?(5 votes)
- Good question! It would be 2 is squared 3 is cubed, 4 is quartic, 5 is quintic, and so on. Here's some more info: https://www.reddit.com/r/askscience/comments/3rchs6/if_2_is_squared_and_3_is_cubed_what_is_4_called/(6 votes)

- How does perimeter help in the real world(6 votes)
- Can the square be even and odd?(4 votes)
- The area of a square can be both even and odd. Take a 7 by 7 square, for example, the side lengths are 7 units, the area is 7*7 (7 times 7) which is equal to 49, which is an odd number. Another example is a 4 by 4 square, 4 times 4 is 16, which is an even number.(5 votes)

- Perimeter is the one where you measure the distance around the shape and Area is when you measure the part inside the shape, right? I always get confused.(3 votes)
- Yes, the area is inside the shape and perimeter is around the shape.(7 votes)

## Video transcript

So we've got two
figures right over here, and I want to think about
how much space they take up on your screen. And this idea of how much
space something takes up on a surface, this idea is area. So right when you look at
it, it looks pretty clear that this purple figure
takes up more space on my screen than
this blue figure. But how do we
actually measure it? How do we actually know how much
more area this purple figure takes up than this blue one? Well, one way to do
it would be to define a unit amount of area. So, for example, I could create
a square right over here, and this square, whatever units
we're using, we could say it's a one unit. So if its width right
over here is one unit and its height right
over here is one unit, we could call this
a unit square. And so one way to measure
the area of these figures is to figure out how many
unit squares I could cover this thing with
without overlapping and while staying
in the boundaries. So let's try to do that. Let's try to cover each of
these with unit squares, and essentially we'll
have a measure of area. So I'll start with
this blue one. So we could put 1, 2, 3,
3, 4, 5, five unit squares. Let me write this down. So we got 1, 2, 3,
4, 5 unit squares, and I could draw the
boundary between those unit squares a little bit clearer. So we have 5 unit squares. And so we could say that
this figure right over here has an area. The area is 5. We could say 5 unit squares. The more typical
way of saying it is that you have 5 square units. That's the area over here. Now, let's do the same thing
with this purple figure. So with the purple figure, I
could put 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 of these unit squares. I can cover it. They're not overlapping,
or I'm trying pretty close to not make them overlap. You see, you can fit 10 of them. And let me draw the
boundary between them, so you can see a
little bit clearer. So that's the boundary
between my unit squares. So I think-- there you go. And we can count them. We have 1, 2, 3, 4,
5, 6, 7, 8, 9, 10. So we could say the area
here-- and let me actually divide these with the
black boundary, too. It makes it a little bit
clearer than that blue. So the area here for the
purple figure, we could say, so the area here is equal to 10. 10 square, 10 square units. So what we have
here, we have an idea of how much space does
something take up on a surface. And you could eyeball
it, and say, hey, this takes up more space. But now we've come up with
a way of measuring it. We can define a unit square. Here it's a 1 unit by 1 unit. In the future we'll see that
it could be a unit centimeter. It could be a 1 centimeter
by 1 centimeter squared. It could be a 1 meter
by 1 meter squared. It could be a 1 foot
by 1 foot square, but then we can use
that to actually measure the area of things. This thing has an area
of 5 square units. This thing has an area
of 10 square units. So this one we can actually
say has twice the area. The purple figure
had twice the area-- it's 10 square units--
as the blue figure. It takes up twice the amount
of space on the screen.