Source: Safalta.comYou may also read Area Of A Rhombus
- 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.
The formula of the Perimeter of the Rhombus
The perimeter of a rhombus is given as:
Here, a = Length of the side of the rhombus
The perimeter of the Rhombus Formula With DiagonalsThe 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 bea2a2
and OS will be
Assume that the side of the rhombus is X.
Using Pythagoras theorem in triangle POS, we get:
X2 = a22+b22a22+b22, which gives us,
Substitute the value of X in the perimeter of the rhombus formula i.e. 4X. You will get:
6. So, the perimeter of the rhombus will be equal to 2 ×(a2+b2)−−−−−−−√(a2+b2)
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Question: Find the perimeter of a rhombus having a side of 5 cm.
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?
|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)|