Area of Square
The area of a square is defined as the number of square units needed to fill this shape. In other words, the area of a square is the region occupied within its boundary. When we want to find the area of a square, we consider the length of its side. Since all the sides of the shape are equal, its area is the product of its two sides. The common units used to measure the area of the square are square meters, square feet, square inches, and square cm.
The area of a square can also be calculated with the help of other dimensions, such as the diagonal and the perimeter of the square. Let us learn more about the area of square and the formula of area of square on this page.
| 1. | What is the Area of Square? |
| 2. | Area of Square Formula |
| 3. | How to Find Area of a Square? |
| 4. | FAQs on Area of a Square |
What is the Area of Square?
A square is a closed two-dimensional shape with four equal sides and four equal angles. The four sides of the square form the four angles at the vertices. The sum of the total length of the sides of a square is its perimeter, and the total space occupied by the shape is the area of the square. It is a quadrilateral that has the following properties.
- The opposite sides of a square are parallel.
- All four sides of a square are equal.
- All angles of a square measure 90º.
Squares can be found all around us. Here are some commonly seen objects which have the shape of a square. The chessboard, the clock, and a blackboard, are all examples of a square.
Area of a Square Definition
The area of a square is the measure of the space or surface occupied by it. It is equal to the product of the length of its two sides. Since the area of a square is the product of its two sides, the unit of the area is given in square units.
Observe the square given below. It has occupied 25 squares. Therefore, the area of the square is 25 square units. From the figure, we can observe that the length of each side is 5 units. Therefore, the area of the square is the product of its sides. Area of square = side × side = 5 × 5 = 25 square units.
Square Definition
A square is a quadrilateral in which all four sides are equal and parallel to each other. All the angles in a square are 90 degrees.
Area of Square Formula
The formula for the area of a square when the side is given is:
Area of a square = Side × Side = S2
Algebraically, the area of a square can be found by squaring the number representing the measure of the side of the square. Now, let us use this formula to find the area of a square of side 7 cm. We know that the area of a square = Side × Side. Substituting the length of side as 7 cm, 7 × 7 = 49. Therefore, the area of the given square is 49 cm2.
The area of a square can also be found with the help of the diagonal of the square. The formula used to find the area of a square when the diagonal is given is:
Area of a square using diagonals = Diagonal2/2.
Let us understand the derivation of this formula with the help of the following figure, where 'd' is the diagonal and 's' represents the sides of the square.
Here the side of the square is 's' and the diagonal of the square is 'd'. Applying the Pythagoras theorem we have d2 = s2 + s2; d2 = 2s2; d = √2s; s = d/√2. Now, this formula will help us to find the area of the square, using the diagonal. Area = s2 = (d/√2)2 = d2/2. Therefore, the area of the square is equal to d2/2.
How to Find the Area of a Square?
We can find the area of a square using different methods depending on the values that are given to us. Let us see the different ways in which we can find the area of a square when the perimeter is given, when the sides are given, or when the diagonal is given.
Area of Square when the Perimeter of a Square is Given
Example: Find the area of a square park whose perimeter is 360 ft.
Solution:
Given: Perimeter of the square park = 360 ft
We know that,
Perimeter of a square = 4 × side
⇒ 4 × side = 360
⇒ side = 360/4
⇒ side = 90 ft
Area of a square = side2
Hence, Area of the square park = 902 = 90 × 90 = 8100 ft2
Thus, the area of a square park whose perimeter is 360 ft is 8100 ft2
Area of Square When the Side of Square is Given
Example: Find the area of a square whose side is 6 cm.
Solution:
Given: Side of the square = 6 cm
We know that,
Area of a square = Side2
Hence, Area of the square = 62 = 6 × 6 = 36 cm2
Area of Square When the Diagonal of a Square is Given
Example: Find the area of a square whose diagonal is 12 cm.
Solution:
Given: Diagonal of the square = 12 cm
We know that,
Area of a square formula when diagonal is given = d2/2
Hence, Area of the square = (12 × 12)/2 = 72 cm2
Tips to Find Area of Square
Note the following points which should be remembered while we calculate the area of a square.
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A common mistake that we tend to make while calculating the area of a square is doubling the number. This is incorrect. Always remember that the area of a square is side × side and not 2 × side.
- When we represent the area, we should not forget to write its unit. The side of a square is one-dimensional and the area of a square is two-dimensional. Hence, the area of a square is always represented as square units. For example, a square with a side of 3 units will have an area of 3 × 3 = 9 square units.
☛ Related Articles
- Diagonal of Square
- Area of Squares and Rectangles Worksheets
- Perimeter of Square
- Surface Area of a Square Prism
- Area of Square Calculator
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FAQs on Area of Square
What is Area of Square in Geometry?
The area of a square is defined as the number of square units that make a complete square. It is calculated by using the area of square formula: Area = side × side, and the answer is given in square units.
What is the Area of a Square Formula?
When the side of a square is given, then we calculate the area of the square using the formula, Area of square with side 's': Area = s × s = s2. When the diagonal 'd' of the square is given, then the formula used to find the area of a square is, Area = d2/2.
How Do You Calculate the Area of a Square?
The area of a square is calculated with the help of the formula: Area = s × s, where, 's' is one side of the square. Since the area of a square is a two-dimensional quantity, it is always expressed in square units. For example, if we want to calculate the area of a square with side 4 units, it will be: A = 4 × 4 = 16 unit2. Check area of square calculator for quick calculations.
What are the Area and Perimeter of Square Formulas?
The perimeter of a square is a sum of the four sides of a square that is Perimeter = 4 × Side. It is given in terms of m, cm, ft, and inches.
The area of square = Area = s × s, where, 's' is one side of the square. It is given in terms of m2, cm2, ft2, and in2.
Check:
How to Find the Area of a Square From the Diagonal of a Square?
The area of a square can also be found if the diagonal of a square is given. The formula that is used in this case is: Area of a square using diagonals = Diagonal²/2. For example, the diagonal of a square is 6 units, the Area = 6²/2 = 36/2 = 18 square units.
How to Find the Area of a Square From the Perimeter of the Square?
The area of a square can be calculated if the perimeter of the square is known. Since the perimeter of a square is: P = 4 × side, we can find the side of the square 's' = Perimeter/4. After getting the side, the area of a square can be calculated with the formula: A = s × s. For example, if the perimeter of a square is 32 units, we will substitute this value in the formula: P = 4 × side. 32 = 4 × side. So, the side will be 8 units. Now, we can calculate the area of the square with side 8 units. Area = s × s = 8 × 8 = 64 square units.
What are the Units of the Area of a Square?
The area of a square is a two-dimensional quantity, therefore, it is always expressed in square units. The common units of the area of a square are m2, inches2, cm2, and ft2.
What is the Area of a Square Inscribed In a Circle?
If a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. So, if the diameter of the circle is given, this value can be used as the diagonal of the square, and the area of the square can be calculated with the formula: Area of a square using diagonals = Diagonal²/2.
Find the Side of a Square whose Area is 36 Square Units.
If the area of a square is 36 square units, the side of the square can be calculated using the same formula and by substituting the given value. We know that the area of square = side2. After substituting the value of the area as 36 we have 36 = side2. So, side = √36 = 6 units.
What is the Side of Square Formula when Area is Given?
When the area of a square is given, then the side of square formula is, Side of square = √(Area of square). For example, let us find the side of a square whose area is 2304 square units. After substituting this value in the formula, we get, Side of square = √2304 = 48 units. Therefore, the side of the square is 48 units.
What is Perimeter and Area of Square?
The perimeter of a square is the length of the total boundary of the square. If we know one side of a square we can find its perimeter using the formula, Perimeter of square = 4 × side. The area of a square is the total region occupied within its boundary. If we know one side of a square we can find its area using the formula, Area of square = side × side.