The Formula of Area of Square Overview
The number of square units required to fill a square is known as its area. In other terms, the area of a square is the space enclosed by its perimeter. When calculating the area of a square, we consider the length of its sides. Because the shape's sides are all equal, its area equals the product of its two sides. The most popular units for measuring square area are square meters, square feet, square inches, and square cm. Other dimensions, such as the diagonal and the perimeter of the square, can also be used to compute the area of a square. There are predefined formulas for calculating the area of squares, rectangles, circles, triangles, and so on.
What is a Square?
A square is a quadrilateral with four equal sides that are parallel to each other. A square's angles are all 90 degrees. A square is a two-dimensional closed form that has four equal sides and four equal angles. The four angles at the vertices are formed by the square's four sides. The perimeter of a square is the sum of the entire lengths of its sides, and the area of the square is the total space filled by the form.
Area of Square Formula: Examples
Squares may be found in a variety of products and all around us in everyday life. Bread slices, chessboards, photo frames, pizza boxes, and other square-shaped products are examples.
The Formula of Area of Square: Properties
Square is a quadrilateral with the following characteristics-
- A square's angles are all 90°.
- A square has four equal sides.
- A square's opposite sides are parallel.
- Squares may be found everywhere.
What is Area in Maths?
The area of a form is a measurement of how much space it has within it. In ordinary life, calculating the area of a form or surface can be important; for example, you may need to know how much paint to buy to cover a wall or how much grass seed to spread to sow a lawn.
What is the Area of Square?
The area of a square is the amount of space or surface it takes up. It is equal to the product of its two sides' lengths. Because the area of a square is the product of its two sides, the area unit is in square units. The units of square area are square meters (m²), square centimeters (cm²), square feet (ft²), square inches (in²), and so on.
What is the Formula of Area of Square?
When the side is specified, the formula for calculating the area of a square is-
Area of a Square = Side x Side = S²
When the diagonal is known, the formula for calculating the area of a square is-
Area of a Square using diagonals = Diagonal²/2
Read more about the Father of Mathematics.
Area of Square Formula: Conversion Units
Some unit conversion lists are given below-
- 1 m = 100 cm
- 1 sq. m = 10,000 sq. cm
- 1 km = 1000 m
- 1 sq. km = 1,000,000 sq. m
Derivation of the Formula of Area of Square
Algebraically, the area of a square may be calculated by squaring the integer indicating the length of the square's side. Apply this formula to calculate the area of a 25 cm². We know that the area of a square = Side x Side
So, 25 x 25 = 625
When the side length is substituted as 25 cm. As a result, the specified square has an area of 625 cm².
The diagonal of a square may also be used to calculate the area of a square. For Example: The formula's derivation using the diagram below, where 'd' represents the diagonal and ‘s' represents the square's sides. Using Pythagoras' theorem,
We get,
d² = s² + s²
d² = 2s²
d = √2s
s = d/√2
Therefore, this formula will now assist us in determining the area of the square using the diagonal. Area equals s² = (d/√2)²
d²/2
As a result, the square's area equals d²/2.
Read more about the Area of Parallelogram.
How to Calculate the Area of a Square?
Depending on the data provided, we may calculate the area of a square using a variety of approaches. There are many methods for calculating the area of a square when the perimeter, sides, and diagonal are all supplied. They are as follows-
Area of Square Formula: When the Perimeter of a Square is Given
Example: Find the area of a square park with a 276 ft. perimeter.
The perimeter of Square Park = 276 ft.
The perimeter of a Square = 4 x side
=> 4 x side = 276
=> side = 276/4
=> side = 69 ft.
Area of Square = side²
Therefore, the area of the square park = 969)²
= 69 x 69
= 4,761 ft²
Thus, the size of a square park with a 276 ft. perimeter is 4,761 ft².
Read more about the Perimeter of a Cuboid.
The formula of Area of Square: When the Side of the Square is Given
Example: Determine the area of a square with a side length of 21 cm.
Side of Square = 21 cm
Area of Square = side²
Therefore, the area of the square park = (21)²
= 21 x 21
= 441 cm²
Hence, the area of the square is 441 cm².
Area of Square Formula: When the Diagonal of the Square is Given
Example: Determine the area of a square with a diagonal of 66 cm.
Diagonal of Square = 66 cm
Area of a square when diagonal = d²/2
= (66)²/2
= 4356/2
= 2,178 cm²
Hence, the area of the square is 2,178 cm².
Points to Remember
- When determining the area of a square, it is usual practice to double the value. This is untrue. Always remember that the area of a square is side by side, not two by two.
- When we portray an area, we must remember to include its units.
- A square's side is one-dimensional, while its area is two-dimensional.
- As a result, the area of a square is always expressed in square units.
- A square with a side of 3 units, for example, has an area of 3 x 3 = 9 square units.
Sample Questions for the Formula of Area of Square
Sample Question 1: Determine the area of a square clipboard with a side length of 360 cm.
Solution: Side of the square clipboard = 360 cm = 3.6m
Area of clipboard = Side x Side
= 360 cm × 360 cm
= 129600 sq. cm
= 1.294 sq. m
Sample Question 2: A square wall has a side length of 55 meters. What is the cost of painting it at Rs. 9 per square meter?
Solution: Side of the wall = 55 m
Area of the wall = Side x Side
= 55 m × 55 m
= 3,025 sq.m
The cost of painting for 1 sq. m = Rs. 3
Therefore, the cost of painting for 3,025 sq. meters = Rs. 3 x 3,025
= Rs 9,075
Sample Question 3: The floor of a courtyard 90 m long and 30 m broad will be covered with square tiles. Each tile has a 6 m side. Determine the number of tiles needed to cover the floor.
Solution: Length of the floor = 90 m
Breadth of the floor = 30 m
Area of the floor = Length × Breadth
= 90 m × 30 m
= 2700 sq. m
Side of one tile = 6 m
Area of one tile = Side × Side
= 6 m × 6 m
= 36 sq. m
No. of tiles required = area of floor/area of a tile
= 2700/49
= 75 tiles
Practice Questions for the Area of Square Formula
Q.1 Find the area of the square whose diagonal length is 27 cm.
Q.2 The square garden has a total size of 423 m2. Determine the length of the garden.
Q.3 Determine the length of an 1800 square meter park.
Q.4 An 85-meter-long square wall must be painted. If painting costs ₹7.50 per square meter, determine the cost of painting the entire wall.
Q.5 What is the area of a square table with a 9-foot diagonal?