Quadrilateral is defined as the four-sided polygon, having four vertices and four angles thus formed by joining four non-collinear points. For any polygon to be a quadrilateral it must satisfy two conditions: the sum of all the four interior angles should be 360 and it should be a closed figure with 4 sides. Properties of Rhombus show that it is a type of Quadrilateral.
There are 5 types of quadrilaterals called Rectangle, Square, Parallelogram, Rhombus, and Trapezium depending upon the properties of their sides and angles.
In order to study rhombus, we need to know little about parallelogram which is a special type of quadrilateral having the opposite sides of equal length and the opposite angles are of equal measure i.e. opposite sides are parallel as well.
What is a Rhombus?
A rhombus is defined as the special type of parallelogram (quadrilateral in which opposite sides are equal and parallel) where it also has four equal sides i.e four all the four sides are of the same length and the opposite sides are parallel. Along with that the diagonals in the case of rhombus also bisect each other at right angles. The rhombus in other words is also known as a diamond or rhombus diamond. In plural form, it is called rhombi or rhombuses.
Properties of Rhombus:
- Rhombus is a type of quadrilateral thus it will have four sides and four angles.
Since the sum of all interior angles of the quadrilateral is 360, thus the sum of all interior angles in the case of rhombus will be 360 as it is a type of quadrilateral itself.
- The opposite sides of the rhombus are parallel to each other thus making the sum of a pair of adjacent angles to be 180 i.e supplementary.
- The diagonals of the rhombus always bisect each other at 90 i.e makes the right angle at the point of bisection.
- The angles of the rhombus are bisected by its diagonals.
- Diagonals of a rhombus have reflection symmetry to the rhombus.
- Four right-angled triangles are formed by the diagonals of the rhombus which are congruent to each other.
- Quadrilateral obtained by joining midpoints of the sides of the rhombus will be a rectangle while we will get another rhombus when we are joining midpoints of half the diagonal.
- There cannot be any circumscribing circle or inscribing circle within a rhombus.
Area and Perimeter of Rhombus
A rhombus is a special type of parallelogram as it satisfies all the properties of a parallelogram. Thus we can say that rhombus also has its two diagonals as its two lines of symmetry, the same as in the case of a parallelogram. The area of the rhombus is defined as the region that it includes or covers in its two-dimensional plane.
Area of Rhombus can be found using,
Area = (diagonal1 x diagonal 2)/2 square units
The perimeter of the rhombus is the length of its total periphery or outer boundaries i.e is in other words it is the sum of the lengths of all sides of the rhombus. Since we know all the sides of the rhombus are of equal length thus the sum of all sides will be four times the size of the rhombus.
Thus, Perimeter of Rhombus = 4(Side)
Square a Special Type of Rhombus:
Square is a special type of rhombus as it has all its equal and opposite sides parallel to each other. In the case of square, all angles should be 90 which is not necessary in the case of a rhombus. Since the square satisfies all the properties of the rhombus thus it can be termed as a special type of rhombus.