Main content

### Course: 3rd grade > Unit 10

Lesson 6: Decompose figures to find area# Decomposing shapes to find area: grids

Lindsay finds the area of an irregular shape by decomposing it into 2 rectangles. Created by Lindsay Spears.

## Want to join the conversation?

- How is this important to us?(11 votes)
- This could be useful to many job purposes. One example is being an architect. Suppose you need to design a house for efficiency and low cost. Part of the house that you are building might be in an irregular shape style. You would have to know the area of it because it could help you put things like a bed inside. If you just randomly make a house with no blueprints or area models, you definitely would mess up. You could make a room too small or forget to place a door. There are many more ways that math can help us in our life, but this is just one of them. Hope this helped! -Johnny Unidas(26 votes)

- Hello I don't understand what do we do when grids are not there(1 vote)
- Usually, if a grid is not present, some sort of measurements is on the object in the shape of distances, say
`1cm`

or`3cm`

on a length or a width that you can use. So do not worry about that, you can and will be able to find the area.*Hope this helps!*(1 vote)

- How does it cover 2 sq cm?(0 votes)
- The shape does not cover
`2cm²`

, the total area is`24cm²`

as the two shapes have the areas of`14cm`

and`10cm`

adding to the total area of the shape.

It does this through the following multiplication and addition sequences:`5cm`

x 2cm

———————

10cm²

This is the area of the first one of the shapes, a total of`10cm²`

`2cm`

x 7cm

————————

14cm²

This is the area of the second one of the shapes, a total of`14cm²`

Now, what we have to do is add both the numbers up to get the total area:`14cm²`

x 10cm²

————————

24cm²

So, therefore, we can make the conclusion that the area of both the shapes combined are**24cm**².*Hope this helps!*(1 vote)

- How come you have to divide it?Because I no I don’t(0 votes)

## Video transcript

- [Voiceover] Each small
square in the diagram has a side length of one centimeter. So, what is the area of the figure? So, we have this figure down here in blue, and we want to know its area. Area is the total space it covers. And, we're also told that
each of these little squares has a side length of one centimeter. So, that means that each of these squares is one square centimeter. So, we can find the area by seeing how many square centimeters
does this figure cover? One way would be to just try to draw the little square
centimeters and count them. There's one square
centimeter, there's two, and so on and keep counting them all the way through. Or, what we could do is we could look at this and try to break it into two shapes. So we can say down here, into two rectangles. Down here we have one rectangle, and up here we have a second rectangle. And then we can find the
area of each rectangle and add it together to find the total area that the figure covers. Down here on the bottom, we have two rows of unit squares. And each of those has one, two, three, four, five, six, seven. So, one, two, three,
four, five, six, seven. So there's two rows of seven unit squares, or seven square centimeters, so the bottom rectangle is made
up of 14 square centimeters. It covers 14 square centimeters. And the top rectangle, let's see we have one row,
two, three, four, five rows. And each of those rows has
one, two square centimeters, so we have five rows of two
square centimeters, or 10. So, this top rectangle
here that we have in blue covers 10 square centimeters, plus the bottom rectangle
that we outlined in green covers 14 square centimeters, so in total, the entire figure covers 24 square centimeters. So, 24 square centimeters is our area, because area is how much
space does it cover, and we figured out that it
covered 24 square centimeters.