Education

Understanding the Properties, Formulas of Rhombus in Mathematics

September 9, 2021

4 mins

A type of quadrilateral is basically known as a rhombus. A distinct case of a parallelogram, at 90 degrees the diagonals of which intersect amongst themselves. Having the shape of a diamond, it is also known as a rhombus diamond and this is the elementary property of a rhombus. A rhombus is also known as a four-sided quadrilateral. The opposite sides are parallel to each other and opposite angles are always equal. Furthermore, all four sides of a rhombus are equal length-wise, and they diagonally bisect each other at the right angles. The rhombus is known as rhombi or rhombuses plurally.

You all must have seen playing cards and the diamond shape in them. All the rhombuses are kites and parallelograms. If all the angles of the rhombus are at 90 degrees, then it’s called a square.

Now, before going to anything else we need to understand what is a quadrilateral? A quadrilateral is called a polygon, it encloses four angles, and contains four sides and four vertices. The total of the angles in the interior is 360 degrees. There are six kinds of quadrilaterals and they are as follows:

Rhombus
Kite
Square
Rectangle
Trapezium
Parallelogram

Table of Contents

Let’s look at some important points about the angles in a rhombus:

The total of interior angles is four.
Total calculation of interior angles sums up to 360 degrees.
The angles that are opposite to each other are always equal.
The adjacent angles are supplementary.
The diagonal bisect each other at right angles.

The formula for the calculation of rhombus has two important characteristics:

Perimeter
Area

For calculating the Area, area of rhombus = A, diagonals are d1 and d2 and the result of the product that we get after multiplying the diagonals is divided by 2, as per rule. The formula that we get is

The area of Rhombi will be, A = (d1 x d2)/2 square units

Similarly, the perimeter is the total of all the sides of a rhombus. Suppose P is the perimeter and a are the angles. So, the formula would be

Perimeter, P = 4a units

The properties of a rhombus are used for solving a lot of mathematical problems, some of the most important ones are mentioned below:

All four sides are equal.
The sides opposite are parallel to each other.
The opposite angles are equal.
The bisection of diagonals is at right angles.
Angles that are adjacent sum up to180 degrees.
Four right-angled triangles are formed with two diagonals and to each other they are congruent.
On joining the midpoint of the sides, you get a rectangle.
On joining the midpoints of half of the diagonal, you get one more rhombus.
No confining circles should be surrounding the rhombus.
No inscribing circle could be there inside a rhombus.
When the diagonal which is short is equal to one side, they form two congruent symmetrical triangles.
On the axis of rotation, when you revolve a rhombus on any side, you get a cylindrical surface that has two ends, one convex cone, and the other concave cone.
On the axis of rotation, when you revolve a rhombus on the line that joins the midpoint of opposite sides, you get a cylindrical surface that has two ends, both have concave cones.
When the rhombus revolves about the diagonal that is long on the axis of rotation, you get a solid as the two cones are attached to bases. In this situation, the maximum diameter of the solid equals the diagonal that is short.
When the rhombus revolves about the diagonal that is short on the axis of rotation, you get a solid as the two cones are attached to bases. In this situation, the maximum diameter of the solid equals the diagonal that is long.