The area of a square is equal to side × side or A = s × s = s², where “s” is the length of one side. Let’s see some examples.
Content:
- Formula for the area of a square.
- Formula for the area of a square using diagonals
- Example 1.
- Example 2.
- Example 3.
- Example 4.
- Example 5.
- FAQ
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Formula for the area of a square
The formula for the area of a square is:
Where “s” is the length of one side:
Formula for the area of a square using diagonals
The formula for the area of a square when the diagonal “d” is given, is:
Where “d” is the length of one diagonal:
Remember that the area is always expressed in square units, such as in², ft², cm², m², etc.
Example 1
Find the area of a square with sides 2 meters long.
We will use the classic formula:
The area of the square is 4 square meters, which can be written as 4 m². If you have any doubt, the image below can help you a little.
Example 2
Find the area of a square with sides 6 feet long.
Remember the classic formula:
The area of the square is 36 ft².
Example 3
What is the area of a square whose diagonal is 10 feet?
In this example, we will use the formula when the diagonal is given:
The area of the square is 50 square feet, which can be written as 50 ft². The image below may be helpful.
Example 4
Find the area of the square shown below.
The side length is 13 inches, therefore, we will substitute 13 in for side (s) in the formula:
Remember that area is measured in square units; therefore, the area of this square is 169 square inches, which can be written as 169 in².
Example 5
The perimeter of a square is 36 meters. What is the area of the square?
Remember that the perimeter is the sum of the length of all the sides of the square: s + s + s + s, or 4×s:
Then we calculate the area of the square using the classic formula for the area of a square:
The area of the given square is 81 m².
FAQ
What is the area of a square?
The area of a square is equal to side × side, or A = s × s = s², where “s” is the length of one side. For example, the area of a square with each side 5 meters long is 5 m × 5 m = 25 m².
What is the perimeter of a square?
The perimeter of a square is the sum of the length of all the sides of the square: side + side + side + side, or 4 × side. For example, the perimeter of a square with each side 6 feet long is: 6 ft + 6 ft + 6 ft + 6 ft = 24 ft.
What is area?
Area is a measure of the amount of surface in a region. You can use area to describe the size of a national park, a lake, a farm or a parking lot. Recall that area is always measured in square units, such as in², ft², cm², m², etc.
What is the perimeter and area of a square?
The perimeter of a square is: P = 4 s, and the area of a square is A = s × s = s², where “s” is the length of one side. You can also check the formulas in this image:
That’s all for today, see you next class.