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What Are the Metric Units for Area?

This entry uses the metric system. For the imperial system click here.

When you want to describe the size of a surface, you are talking about an area. Examples of this are the size of a floor, a piece of paper, or a wall. How many doormats can you fit on the floor of your living room? How many pieces of paper can you fit in the hallway? How many towels can you fit on the floor of your bedroom?

The math master measuring the size of a room using towels

Because towels can come in many different sizes, it can be difficult to agree on how big a surface is if you measure it in the number of towels you can put on it. Which towel should you use? A bath towel or a kitchen towel? Because there isn’t any standard towel size, we agreed to use a square with one meter on each side. We call this square a square meter. Because we all agree on the length of a meter, we also agree on the size of the square meter.

Two rooms measured with square meters

Area is measured in square meters (m2). A square meter is as large as a square where every side has a length of one meter. If you want to measure the area of smaller things, you can use square centimeters (cm2). Below you can see an example of an area with a size of 1 m2.

A square with side lengths of 1m

You can also have surfaces with an area of 1 cm2. The figure below is an example of this. It has a length and width of 1 cm2 each.

A square with side lengths of 1cm

You might have already learned that 1 m is the same as 100 cm. But 1 m2 is not the same as 100 cm2. There’s actually space for 10000 squares of 1 cm2 in the first figure with size 1 m2. Take a look at the figure below. You can see that the blue square (1 cm2) can fit 100 times into the white square. The white square can fit 100 times into the pink square, which has the size 1 m2. That means that there is space for 100 100 = 10000 of the blue squares (1 cm2) in the pink square of 1 m2.

10000 squares with sides of 1cm inside a square with sides of 1m

Example 1

Eric is going to paint the pattern below on one of the walls at his school, and he has to calculate how much paint he needs.

Squares painted in a specific pattern where each square is one square meter

If every square is 1m2, how many square meters of paint does he need for every color?

Eric needs 8 m2 of purple paint, 8 m2 of pink paint, 8 m2 of orange paint, 8 m2 of red paint, 16 m2 of blue paint and 16 m2 of green paint.

Example 2

Cathy needs to cut out the pattern below from colored pieces of paper.

Squares painted in a specific pattern where each square is one square centimeter

How many square centimeters of paper does she need of each color if each square is 1cm2?

Cathy needs 7 cm2 of yellow paper, 7 cm2 of purple paper and 67 cm2 of blue paper.

So, if you want to measure smaller surfaces, you can use square decimeters, square centimeters or square millimeters. If you want to measure larger surfaces, you can use square kilometers. As one meter is ten decimeters, one square decimeter (dm2) is a square with sides equal to one tenth of a meter (a decimeter). You might think that one square meter has space for ten square decimeters. But that’s not the case! You can fit 100 square decimeters in one square meter. You can see the reason for this in the figure below.

In the same way, one square centimeter (cm2) is a square where each side has a length of one hundredth of a meter (one centimeter). As there are 100 cm in a meter, you can fit a whole 100 100 = 10000 square centimeters in a square meter.

10000 squares of sides 1cm fit in a square of sides 1m

Similarly, one square millimeter (mm2) is a square where each side has a length of one thousandth of a meter (one millimeter). As there are 1000 mm in a meter, you can fit a whole 1000 1000 = 1000000 square millimeters in a square meter!

1000000 squares with sides of 1mm fit in a square with sides of 1m

When you need to measure the surface of really big surfaces, for example cities and countries, it can be smart to use larger units. In that case, the unit square kilometers (km2) is often used. A square kilometer is a square where each side has a length of a thousand meters (one kilometer).

Conversion between different units of area

Notice how I write and do calculations with units. I begin by writing down the expression. Then I check the bubble figure to see what I have to divide or multiply by to get to the unit the exercise asks for. Then, I solve the exercise step by step. The trick is to switch the unit in the expression with this: The multiplication or division sign (depending on which way I’m moving in the bubble figure), the number the bubble figure shows me, and the corresponding unit. In that way, I can work my way through the bubble figure until I get where I need to go.

Example 3

Square meters to square decimeters:

4m2 = (4 100)dm2 = 400dm2

Square millimeters to square centimeters:

4000mm2 = (4000 ÷ 100)cm2 = 40cm2

Square decimeters to square centimeters:

40dm2 = (40 100)cm2 = 4000cm2

Square centimeters to square decimeters:

400cm2 = (400 ÷ 100)dm2 = 4dm2

Square centimeters to square millimeters:

400cm2 = (400 100)mm2 = 40000mm2

Square decimeters to square meters:

400dm2 = (400 ÷ 100)m2 = 4m2

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