Perimeter of Rhombus


 
 
Concept Explanation
 

Perimeter of Rhombus

Perimeter of A Rhombus:

First, all four sides of a rhombus are equal, meaning that if we find one side, we can simply multiply the side by four to find the perimeter.

Second, the diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half. Using Pythagorean Theorem on any one of them will give us the length of our sides.

Illustration: If the area of rhombus be 24 cm^{2}  and one of its diagonals be 4 cm, find the perimeter of rhombus.

Solution :Let  ABCD be a rhombus such that its one diagonals AC = 4 cm. Support the diagonals AC and BD intersect at O. We have, Area of rhombus ABCD = 24 cm^{2}

large Rightarrow Rightarrow frac{1}{2}times 4times BD= 24

Hence BD = 12cm. Thus,  we have AC = 4 cm and  BD = 12 cm

large thereforeOA=frac{1}{2}AC=2 cm      and OB=frac{1}{2}BD=6 cm

Since the diagonals of a rhombus bisect each other at right angle. Therefore, large Delta OAB  is right triangle, right angled at O. Using Pythagoras theorem in large Delta AOB, we have

AB^{2} = OA^{2}  +  OB^{2} 

large Rightarrow AB^{2}  =  2^{2}  +  6^{2} = 4 + 36   = 40 

Rightarrow AB =sqrt{40}cm =2sqrt{10}cm

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Sample Questions
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Question : 1

The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm. Then the area of the rhombus is __________________.

 

Right Option : D
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Explanation
Question : 2

The area of a rhombus is 28 cm^2 and one of its diagonals is 4 cm. Its perimeter is ______________________.

Right Option : A
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Explanation
Question : 3

Calculate the perimeter of a rhombus with each side measuring 5 units.

Right Option : C
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Explanation
 
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