Rhombus

Almost every one of us knows that Rhombus is a quadrilateral, and therefore, just like other quadrilaterals such as square, rectangle, etc., has four vertices and four edges enclosing four angles. Nevertheless, this is not all. There's much more to know about this amazing 2D shape that acts as a crucial part of mathematics, one of the core subjects that walk with us from school to higher education. So, let's get familiar with all the crucial aspects of Rhombus, which includes the properties, angles, its sides and its two diagonals. 

Rhombus Definition

In Euclidean geometry, a rhombus is a special type of quadrilateral that appears as a parallelogram whose diagonals intersect each other at right angles, i.e., 90 degrees. As the shape of a rhombus is just like that of a diamond, it is also known as diamond. The diamond-shaped figure in the playing cards is one of the best examples of a rhombus. Moreover, possibly all the rhombi are kites and parallelograms, but if all angles of a rhombus measure 90°, then it is a square.   

In other words, a rhombus is a special type of parallelogram in which opposite sides are parallel, and the opposite angles are equal. Besides having four sides of equal length, a rhombus holds diagonals that bisect each other at 90 degrees, i.e., right angles. The diagonals are not equal, one is shorter and another is longer. The angles opposite to the longer diagonal are greater than angles opposite to the shorter diagonal 

Where can we find the Rhombus shape in day to day life?

The shape of the Rhombus is around at all times. From the shape of Kaju Katli to the shape of a diamond. From the shape of a Kite to the shape of jewellery, the application of Rhombic shape is very much around. Signboards of the shops, key chains, tiles, gardening tools, baseball grounds etc are in the shape of a Rhombus.  The Rhombus shape is also used in a number of famous architectures over the world. The reason for such huge use of the Rhombic shape is because Rhombus has a very elegant and pleasant shape and is symmetric. The shape of the Rhombus is also geometrically viable because of the fact that all four sides of the Rhombus are equal.  

Angles of Rhombus

Any rhombus includes four angles, out of which the opposite ones are equal to each other. Moreover, the rhombus consists of diagonals that bisect each other at right angles. In other words, we can say that each diagonal of a rhombus cuts the other into two equal parts, and the angle formed at their crossing points measure 90°. There are four interior angles of the Rhombus and since the sum of two opposite sides is 180 degrees, the total sum of the four interior angles of the Rhombus adds up to 360 degrees. The diagonals also bisect the opposite angles of the rhombus, which means that each diagonal of the Rhombus divides the Rhombus into two triangles which are congruent to each other. 

Rhombus Formulas

Formulas for any rhombus are defined while concerning the two main attributes like area and perimeter.

Area of Rhombus

The area of a rhombus refers to the region covered by it in a 2D plane. Based on this definition, the formula for the area of a rhombus is equal to the product of its diagonals divided by 2, and can be represented as:

Area of Rhombus (A) = (d1 x d2)/2 square units

The formula is simple and very easy to understand. The formula is similar to the formula for the area of a triangle, except the fact that instead of  base and altitude, it takes into consideration the two diagonals of the Rhombus

Perimeter of Rhombus

The perimeter of a rhombus is defined as either the total length of its boundaries or the sum of all the four sides of it. Hence, the formula for the perimeter of a rhombus can be represented as: 

The perimeter of Rhombus (P) = 4a units, where ‘a’ is the side of the rhombus.

This formula is similar to the formula for the perimeter of a Square, the length of four sides of the Rhombus is added together and the resulting total length is equal to the perimeter of the Rhombus 

Properties of Rhombus

Now, have a look at some of the significant properties of the rhombus. 

• All four sides are equal in length

• Opposite sides are parallel

• Opposite angles are equal 

• Diagonals bisect each other at right angles, i.e., 90 degrees

• Rhombus's diagonals bisect its opposite angles 

• The sum of two adjacent angles is supplementary, i.e., 180° 

• In a rhombus, the two diagonals form four right-angled triangles that are congruent to each other

• On joining the midpoint of the sides of a rhombus, you will get a rectangle

• If you join the midpoints of half the diagonals, you will get another rhombus

• There can be no circumscribing circle around a rhombus 

• There can be no inscribing circle within a rhombus

• If the shorter diagonal of a rhombus is equal to one of its sides, you will get two congruent equilateral triangles 

• When a rhombus is revolved about the line that joins the midpoints of the opposite sides as the axes of rotation, a cylindrical surface with concave cones on both the ends is formed. 

• When a rhombus is revolved around any of its sides as the axes of rotation, a cylindrical surface with a concave cone at one end and convex cone at another end are formed.

• If the rhombus is revolved about its longer diagonal as the axis of rotation, then a solid having two cones attached to its bases is formed. In this case, the maximum diameter of the shape (solid) will be equal to the rhombus's shorter diagonal. 

• When the rhombus is revolved about its shorter diagonal as the axis of rotation, then you will obtain a solid shape with two cones attached to its bases. The maximum diameter of the solid obtained in this case will be equal to the longer diagonal of the rhombus. 

• When the midpoints of all the four sides of a rhombus are joined with each other, you will obtain a rectangle whose length and width will measure half of the value of the prime diagonal. Moreover, the area of the rectangle formed in this case will be half of the rhombus.

Conclusion

To sum it up, the shape of the Rhombus is symmetric along its diagonals which means that there is an equal area along both sides of the diagonals. That is, if we divide the Rhombus along any of its diagonals, we will get symmetric shapes of equal area and equal perimeter. The symmetric property of the Rhombus comes mainly from the fact that the two diagonals are equal and they bisect each other.