Every two-dimensional object has an area. For example, every square, rectangle or circle has an area.
The function of surface area units is to quantify or measure the area of objects. Since these are two-dimensional units, they are always expressed in square powers. For example, square centimeter (cm2), square meter (m2), square kilometer (km2), and so on.
Let's analyze a simple exercise:
We have a rectangle that is 10 cm long and 7 cm wide, and we need to calculate its surface area.
In this case, the calculation is quite simple. We will calculate the surface area of the rectangle by multiplying the length by the width, that is, 10cm times 7cm. The result is 70cm2. It's crucial to emphasize that since we multiply cm by cm, the result is given in cm2, meaning cm squared(cm raised to the second power).
Remember, surface area measurements are always to the second power!
Now let's do the same exercise using surface units in cm.
That is:
Each side of the square is1m, which is the same as100cm. Let's calculate the area again:
The area of the square =100cm×100cm=10,000cm2
Or, writing it another way:
S=100cm×100cm=10,000cm2
So the first time, we found that the area of the square is 1 square meter, and the second time the same area is equivalent to 10,000cm2.
We can deduce that:
1m2=10,000cm2
We can make the same calculation directly without drawing. Let's write it this way:
1m2=1m×1m=100cm×100cm=10,000cm2
This way, we can always convert between different measurements of area. Now let’s look at some exercises to help us understand better.
Exercise 1
How many square meters m2 are 50,000cm2?
First, let's recall the exercise we solved previously:
1m2=10,000cm2
Now we can calculate:
10,000cm250,000cm2=5
That means,
1m2=10,000cm2
50,000cm2 are 5m2
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Given a rectangle that measures 2 m by 3m. What is the area of the rectangle in cm2? Calculate it in two different ways.
Let's remember that the formula to calculate the area of a rectangle is base × height.
Solution:
Method A:
Let's draw the rectangle
Let's calculate the area of the rectangle inm2:
A=2m×3m=6m2
That is, we find that the area of the rectangle is 6m2. Only that we have been asked for the area in cm2.
Let's remember that
1m2=10,000cm2
That is,
6m2=6×10,000cm2=60,000cm2
Therefore, the area of the rectangle expressed in cm2 is 60,000cm2
Method B:
Let's draw the rectangle:
In this case, we'll convert the units of measure to cm at this stage. Remember that 1m=100cm.
We'll write this on the rectangle:
Now let's calculate the area by multiplying the base by the height and we'll obtain:
A=200cm×300cm=60,000cm2
So, once again we find that the area of the rectangle expressed in cm2 is 60,000cm2.
If you're interested in this article, you might also find the following articles interesting:
Units of Length
Units of Weight
Units of Time
Monetary Units
Units of Volume
On theTutorela website, you can find a variety of math articles
Examples and exercises with solutions for surface area units or area measurements
Exercise #1
8km2=?m2
Video Solution
Step-by-Step Solution
It's important to remember that in one kilometer there are 1000 meters.
Therefore, if there are 8 kilometers, it means there are 8*1000 meters -
8000 meters.
Answer
8000m2
Exercise #2
0.5m=?cm
Video Solution
Answer
50
Exercise #3
0.6km=?cm
Video Solution
Answer
60,000
Exercise #4
12cm=?dm
Video Solution
Answer
1.2
Exercise #5
291cm2=?m2
Video Solution
Answer
0.0291m2
Review Questions
What is a unit of area?
Area units are those used to measure the area of geometric figures, lands or some two-dimensional objects, that is, those that have two dimensions (length and width).
How many meters does one hectare have?
One Hectare has 10000m2
So if we want to know how many square meters are in 7 hectares, we need to multiply the number of hectares by the number of square meters in one hectare.
Thus 7×10000m2=70000m2
Therefore, 7 hectares is equal to 70000m2.
What is the unit of area in the International System of Units (SI)?
As we saw in this article, there are many area measurements, such as:
km2,hm2,dam2,m2,cm2,dm2 among others, but in the SI, the unit used is the m2