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### Course: 5th grade foundations (Eureka Math/EngageNY) >Unit 5

Lesson 1: Topic A: Foundations

# 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?
• 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.
• 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
• 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.
• how do find the area of a triangle?
• 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.
• how we measure the units squares correctly?
• 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.
• do we have to really use the unit squares to measure it?
• 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.
• How do you find the area of a pentagon?
• 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
• So if a unit^2 is cubed, and a unit^3 is squared, then what do we call a unit^4?
• How does perimeter help in the real world