Square and Rhombus

You must have learned about many figures of various shapes and sizes in Geometry. Squares and rhombuses are two of them, which you must have learned in elementary school. In terms of diagonals, length, forms, and angles, both square and rhombus share some similarities and some variances. Because they belong to the same category as a parallelogram, they share several characteristics. 

Square:

A quadrilateral having four equal sides is known as a square. There are numerous square-shaped objects in our environment. Each square form is distinguished by its equal sides and internal angles of 90 degrees. A square is a four-sided closed two-dimensional form (2D shape). A square’s four sides are all equal and parallel to one another. 

Properties of a square:

A square is a closed form with four equal sides and internal angles equal to 90 degrees. A square can have a variety of characteristics. The following are some of the most important features of a square.

1. A quadrilateral with four sides and four vertices is known as a square. 
2. The square’s four sides are all the same length. 
3. A square’s opposite sides are parallel to one another. 
4. Each vertex of a square has a 90° internal angle. 
5. 360° is the sum of all interior angles. 
6. The diagonals of a square are 90 degrees apart. 
7. The diagonals are all the same length. 
8. A square is sometimes known as a parallelogram because its sides are parallel. 
9. The length of a square’s diagonals is greater than the length of its sides. 
10. The square is divided into two congruent triangles by the diagonals. 

Formula of a square:

Area:

The area of a square is the amount of space it takes up. Chess Boards, square wall clocks, and other square shapes are examples. The area of a square formula can be used to calculate the amount of space occupied by these things. The formula for calculating the area of a square is Area of square = s², where is the square’s side. cm², m², and others are the units in which it is measured. 

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

Rhombus:

A rhombus is a quadrilateral with four sides that is a special case of a parallelogram. A rhombus’s opposite sides are parallel, and its opposite angles are equal. Furthermore, the diagonals of a rhombus bisect each other at right angles, and all of the sides are the same length. A rhombus can also be referred to as a diamond or a diamond rhombus. The plural version of rhombus is rhombuses or rhombusi. 

Properties of rhombus:

The following are some of the rhombus’ key properties:

1. The rhombus has an equal number of sides. 
2. A rhombus’s opposite sides are parallel. 
3. A rhombus’s opposite angles are equal. 
4. Diagonals in a rhombus bisect each other at right angles. 
5. A rhombus’ angles are bisected by diagonals. 
6. 180 degrees is equal to the sum of two neighbouring angles. 
7. A rhombus’s two diagonals generate four right-angled triangles that are congruent with each other. 
8. When you join the midpoints of the sides, you’ll have a rectangle. 
9. When you combine the midpoints of half the diagonal, you’ll get another rhombus. 

Rhombus formulas:

Area of rhombus:

In a two-dimensional plane, the area of the rhombus is the area it covers. The product of a rhombus’ diagonals divided by two equals the area of the rhombus. It’s written like this:

A = (d1 x d2)/2 square units is the area of a rhombus. 

Perimeter of rhombus:

The whole length of a rhombus’s boundaries is its perimeter. The circumference of a rhombus is equal to the sum of its four sides. The formula for calculating its perimeter is:

Rhombus perimeter in P = 4a units

The rhombus diagonals are d1 and d2, and the side is ‘a.’ 

Conclusion:

A square is a rhombus because all of its sides have the same length, much like a rhombus. Even, the square and rhombus diagonals are perpendicular to each other and bisect the opposing angles. As a result, we can call the square a rhombus.