A rhombus is a flat form with four angles that aren't always 90 degrees and four equal sides.
Often referred to as a diamond or diamond-shaped object, a rhombus.
The perimeter of a rhombus is the entire distance traversed along its edge.
Because a square meets all the criteria for becoming a rhombus, we can also refer to it as one. Join Safalta School Online and prepare for Board Exams under the guidance of our expert faculty.
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You may also read Area Of A RhombusRhombus 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.
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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.
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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.
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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)
.
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Solved examples
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?
The perimeter of a rhombus is the sum of all its sides. Since all the four sides of a rhombus are equal, the formula used to find the perimeter of a rhombus is: Perimeter = a + a + a + a = 4a, where 'a' represents the side length of the rhombus.
What is the formula of area and perimeter of rhombus?
Important quadrilateral formulas
| Quadrilateral formulas | Rectangle | Rhombus |
|---|---|---|
| Area | l × b | ½ × d1 × d2 |
| Perimeter | 2 × (l + b) | 4a |
What is a formula of rhombus?
Area of Rhombus Formula.
| Formulas to Calculate Area of Rhombus | |
|---|---|
| Using Base and Height | A = b × h |
| Using Trigonometry | A = b2 × Sin(a) |
Is the perimeter of a rhombus whose diagonals are 16 and 30?
The perimeter of a rhombus whose diagonals are 16 cm and 30 cm is 68 cm.
Are all sides of rhombus equal?
All sides of a rhombus are equal. Here, AB = BC = CD = DA. Opposite sides are parallel in a rhombus. Opposite angles are equal in a rhombus.
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