Rhombus has:
- All sides of equal length.
- Opposite sides have to be parallel.
- The altitude is a distance at right angles between two parallel sides.
- The diagonals of a rhombus bisect each other at 90 degrees.
Related Links-
The formula of the Perimeter of the Rhombus
The perimeter of a rhombus is given as:
P=4×a
Here, a = Length of the side of the rhombus
The perimeter of the Rhombus Formula With Diagonals
The Pythagoras theorem is used to calculate the side length of a rhombus when the length of its diagonals is known. In this case, we employ the rhombus's following properties:- The two diagonals of a rhombus split it into four congruent right-angled triangles.
- The diagonals intersect at right angles.
-
Consider a rhombus PQRS with diagonals a and b, and center O.
-
Pick a triangle, say POS. Since the diagonals of a rhombus bisect each other at right angles, the length of OP will be
a2a2
and OS will be
b2b2
. -
Assume that the side of the rhombus is X.
-
Using Pythagoras theorem in triangle POS, we get:
X2 = a22+b22a22+b22
, which gives us,X2 =
(a2+b2)4(a2+b2)4X =
(a2+b2)2−−−−−−−−√(a2+b2)2-
Substitute the value of X in the perimeter of the rhombus formula i.e. 4X. You will get:
4 ×
(a2+b2)2−−−−−−−−√(a2+b2)2-
6. So, the perimeter of the rhombus will be equal to 2 ×
(a2+b2)−−−−−−−√(a2+b2)
.
You may also read-
Question: Find the perimeter of a rhombus having a side of 5 cm.
Solution:
Given,
a = 5 cm
The perimeter of a rhombus = 4 × a
The perimeter of a rhombus = 4 × 5
The perimeter of a rhombus = 20 cm
How do you find the perimeter of a rhombus?
What is the formula of area and perimeter of rhombus?
Quadrilateral formulas | Rectangle | Rhombus |
---|---|---|
Area | l × b | ½ × d1 × d2 |
Perimeter | 2 × (l + b) | 4a |
What is a formula of rhombus?
Formulas to Calculate Area of Rhombus | |
---|---|
Using Base and Height | A = b × h |
Using Trigonometry | A = b2 × Sin(a) |