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Home > News & Articles > Area of Square: Definitions, Examples, Formula, Properties, Derivations, How to Calculate, Practice, and Sample Questions
Updated on 26th June, 2023 , 10 min read
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.
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.
Square is a quadrilateral with the following characteristics-
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-
When the diagonal is known, the formula for calculating the area of a square is-
Some unit conversion lists are given below-
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
As a result, the square's area equals d²/2.
Read more about the Area of Parallelogram.
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-
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.
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.
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.
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
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
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
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?
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By - Nikita Parmar 2023-08-25 09:48:44 , 11 min readAns. A square is a two-dimensional shape with equal-sized sides. Because all of the sides are equal, the area is length times breadth, which equals side x side. As a result, a square’s area is a side square.
Ans. A square’s area is measured in square units.
Ans. In geometry, the area of the square is a surface measurement. It is computed by dividing the length by the breadth.
Ans. A square is a four-sided two-dimensional figure. It is sometimes referred to as a quadrilateral. The total number of unit squares in the form of a square is defined as the area of a square. In other words, it is the area occupied by the square.
Ans. The formula side x side square units may be used to compute the area of a square.
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