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A square is a four-sided polygon with equal-length sides and 90-degree angles on all four sides. When a plane is sliced through the square from the center, both parts are symmetrical. If “a” is the length of a square’s side, then the area of square equals the product of its length and the breadth i.e a^{2}. The area of a square is the number of square units necessary to fill it. In general, the area is defined as the space inside the perimeter of a flat object or a 2d figure. The measuring is done in square units, with the most common unit being square meters (m2).
What is Area?
Area measures how much space an object occupies. The area of a figure is usually measured in a two-dimensional plane, with only the shape’s surface taken into account. In the case of a square, for example, we only consider the length of one of its sides. The area is measured in square units, such as square centimeters, square feet, and square inches.
Area of Square Formula
In arithmetic, the area of the square can be calculated using the amount of space occupied within the square.
Area of Square = Length(L) × Breadth(B)
Area of Square Formula Derivation
Let’s look at the derivation of the area of square formula in arithmetic to get a better understanding of the subject. Consider a square to be a rectangular object with a length of one unit and a width of one unit. A square’s area can be defined as the district that lies inside its boundaries.
Subsequently, we express region as
Area of Square = Length(L) × Breadth(B)
If “g” is the length of the side of the square then
Area of square = g × g
Area(A) of the square = g^{2} |
Example 1: A square has a side length of 8 m, what is its Area?
Solution:
Area of Square = L * B
= 8 m × 8 m
= 64 m^{2}
∴ Area of Square = 64 m^{2}
Example 2:The area of a square shape table is 2500cm^{2 }.What is the length of its side?
Solution:
Area of the square shape table = 2500cm^{2}
We know Area = side×side = side^{2}^{ }
Substituting the value in the formula
2500cm^{2}= side * side
(side)^{2} = 2500
Side =
Side = 25
∴ Length of the side of the square table is 25 cms
Understanding Perimeter
The perimeter of a shape can be described as the path or boundary that surrounds it in geometry. It can also be described as the total outline length of a particular shape. Here Perimeter of a square equals the sum of all four sides.
The perimeter of a square= sum of all the four sides
= side + side + side + side
= 4 * side
If the length of the side is “ b” then
Perimeter of Square= 4b |
Perimeter of Square
It is the length of the edge of a shape that defines its perimeter. The outline of a shape can also be described as its length. If “ s “ is the length of the side of the square the perimeter of square is the sum of all the four sides ie 4s. The perimeter can also be defined as the outline of a shape.
Example 1: A square box of side 45cm is sealed with tape on the lid. How long is the tape?
Solution: The length of the side of the square box is 45cm.
The length of the tape equals the perimeter of the box
As we know the perimeter of the box = 4 x side
= 4 x 45 cm
= 180 cm.
Thus, the length of the tape is 180cm.
Example 2: If a square has a perimeter of 36 m, what is its side?
Solution:
We know, Perimeter = 4 x side
Side = Perimeter / 4
= 36 / 4 cm
= 9 cm.
Therefore the length of the side is 9 cm.
If you want to learn more about the area and perimeter of square, refer to Cuemath.