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### Course: Geometry (all content)>Unit 7

Lesson 1: Count unit squares to find area

# Measuring area with partial unit squares

Lindsay finds the area of a shape by counting whole and partial unit squares.  Created by Lindsay Spears.

## Want to join the conversation?

• hi my question is what is a foot?
• A foot is equal to 12 inches. A foot is also equal to 30.48cm.
• Could it still work on a different shape?
• so you are counting the squares you see in the quadrolatrul thing
• What about if you have 3 half's
• What about the area covered by the lines drawn is that left out of the calculation or counting?
• this is so hard i don't get it help me
• it looks like stairs
• What is Measuring area with partial unit squares, im confused
• How is area suppose to to be the same as perimeter?Or is it not?
(1 vote)
• Area and perimeter are actually different. Think of area as a garden - it is the dirt inside of the garden. Area describes how much space is inside of a figure.
Perimeter, however, is different. Perimeter describes the outside of a figure. Think of it as a fence around a garden. It basically describes how big of a 'fence' a shape would need.
Hope this helped!
-Coder
• How can we count the partial area of a square?
(1 vote)
• Here's an example:
Okay, so, a partial is 1/2 (half)
So, if there were 2 halves you would add them together, thus making 2/2 which is a whole. For each half there is you need to combine them to make a whole.
6 partials would become 3 wholes.
4 partials would become 2 wholes.
2 partials would become 1 whole, etc.
After you add all the partials together take the number you got from that and add it to the whole units within the square and that's your answer.

## Video transcript

- [Voiceover] Each square on the a grid is unit square with an area of one square centimeter. So each of these squares is one square centimeter. This is one square centimeter, and this is one square centimeter, and so on. And now we're asked, what is the area of the figure? By figure I'm sue they mean this bluish, purplish quadrilateral, and we wanna know its area. And area is talking about how much space the shape covers. How much space does this quadrilateral cover? How many square centimeters does the quadrilateral cover? To figure it out, we could start by counting. Here's one. Here's one square centimeter the quadrilateral covers, and I can keep counting like that, all of the square centimeters that I can see. Here's two, three. Another row's got some here. Four, five, six. Down here, here's seven. Eight, nine. So there's nine full square centimeters. Nine square centimeters, but that's not the entire area. That's not everything it covers. It also covers these small parts, these triangle-shaped little spaces of area, and so we need to count those too. Let's look over here. Let's look, if we drew one of these triangles into a unit square, and then we drew another one on the other half of this unit square, we would see that combined they make one full unit square. So we can do that. We can take this triangle up here, which is half of a unit square and combine it with this half of a unit square. So if we combine these two together, that's one more unit square. Now we have nine full unit squares plus one more. But there's still more of them, so we can keep combining. This half unit square combined with the other one on the bottom makes a second unit square, and finally, there's two more halves here, one, two, which combine to make another whole. So we have nine full unit squares plus, plus three more unit squares that we made by combining. We made one by combining these two, a second unit square with these two, and a third unit square here. So we have nine full unit squares and then three more unit squares we put together, which is a total of 12 square units or 12 square, in this case our unit is centimeters, 12 square centimeters. Our figure, our quadrilateral covers 12 square centimeters, so it has an area of 12 square centimeters.