Square and Rectangle

We learned about squares, rectangles, cubes, cones, cylinders, parallelograms, rhombuses, and other shapes in Geometry. All of these shapes can be divided into two categories: two-dimensional shapes and three-dimensional shapes. A few traits may be found in all of the shapes. However, they have a variety of distinguishing qualities that set them apart from one another. 

Square:

The square is a regular quadrilateral with equal length sides and angles on all four sides. The angles of the square are right angles, or 90 degrees. The square’s diagonals are also equal and bisect each other at a 90-degree angle. A rectangle with two opposite sides of equal length is also known as a square. 

Shape of square:

A square is a four-sided polygon with all four sides equal in length and all angles measuring 90 degrees. The square’s shape is such that if a plane is sliced through it from the centre, both parts are symmetrical. Each half of the square now resembles a rectangle with equal sides on both sides. 

Properties of a square:

The following are the most important properties of a square:

1. Each of the four internal angles is 90 degrees. 
2. The square’s four sides are congruent or equivalent to one another. 
3. The square’s opposite sides are parallel to each other.
4. The square’s diagonals are 90 degrees apart and bisect each other. 
5. The square’s two diagonals are equal in length. 
6. The square has four sides and four vertices.
7. The square’s diagonal divides it into two identical isosceles triangles. 
8. The length of the diagonals exceeds the length of the square’s sides. 

Area and perimeter of a square:

Area:

The area of a square in a two-dimensional plane is the area it covers. The area is equal to the square of the sides, or side squared, in this case. It’s calculated in square units.

Area = side² per square unit

If the length of a square’s side is ‘a,’ then 

Area = a² sq. unit.

Perimeter:

The square’s perimeter is equal to the sum of its four sides. The perimeter is measured in the same unit as the square’s side length.

Perimeter = Side + Side + Side + Side = 4 Side

The square’s perimeter equals four sides.

If the length of a square’s side is ‘a,’ then the perimeter is:

Perimeter = 4a sq. unit 

Diagonal of square:

A square’s diagonal is a line segment that connects the square’s two opposed vertices. We can have two diagonals within a square because a square has four vertices. The square’s diagonals are always greater than its sides. 

Rectangle:

A rectangle is a quadrilateral with parallel sides that are equal to each other and all four vertices that are 90 degrees. It’s also known as an equiangular quadrilateral as a result of this. Because the opposite sides of a rectangle are equal and parallel, it is also known as a parallelogram. 

Shape of rectangle:

A rectangle is a two-dimensional flat shape with two dimensions. We may easily represent a rectangle in an XY plane by using the arms of the x-axis and the y-axis to show the length and width of the rectangle, respectively. 

Properties of rectangle:

The following are the properties of rectangle:

1. There are four sides and four vertices to it. 
2. Each vertex is at a 90-degree angle. 
3. The opposing sides are parallel and equal. 
4. Each other is bisected by a diagonal. 
5. The perimeter of a circle is equal to twice the sum of its length and width. 
6. The product of its length and width equals its area.
7. It’s a four-right-angle parallelogram. 
8. 360 degrees is the sum of all interior angles. 

Perimeter of rectangle:

The perimeter of a rectangle is the total distance covered by the rectangle’s outside boundary. It is counted in units of length. The perimeter formula is as follows:

P (perimeter) = 2 (Length + Width)

Area of rectangle:

The region covered by a two-dimensional shape in a plane is called area. It is based on square measuring units. As a result, the rectangle’s area is equal to the area enclosed by its outside bounds. Its length and width are added together. The area of a rectangle is calculated using the following formula: 

Area = length x breadth

Conclusion:

The main difference between a square and a rectangle is that a square has equal sides on all sides, whereas a rectangle has equal sides on both sides. We learned about squares, rectangles, cubes, cones, cylinders, parallelograms, rhombuses, and other shapes in Geometry.