1043 Views

The perimeter of a rhombus is 104 cm and one of its diagonal is 48 cm. find the area of the Rhombus.


Ashish Yadav 2nd Feb, 2019
Answers (2)
Unnam sreekanth 2nd Feb, 2019

Hello aspirant

I can help you with better information.

As perimer formula =2√(d1^2+d2^2)

From this d2 =73.1

From the above formula calculate d2 value

Now area of rhombus=½(d1+d2)

Finally area=60.55

Try to solve again.

Hope helpful to you

All the best

Thank you

Heena Gagwani 2nd Feb, 2019

Let S be the side of the rhombus.

Therefore perimeter of rhombus will be 4S.

Now 4S = 104.

Therefore, S = 26. One side of rhombus is 26 cms.

Now the diagonals in a rhombus form 4 congruent triangles. Also the diagonals of rhombus are perpendicular, so consider any one triangle and the angle between the diagonals is 90 degrees.

Apply Pythagoras Theorem in the triangle and you will get the following equation :-

(26)^2 = (24)^2 + b^2

[Where b is the half of the length of the other diagonal. This can be done because diagonals of rhombus bisect each other. ] {Since diagonals bisect each other we take 24 by (1/2)*48}

Therefore by solving above equation we get b as 10. Which implies length of other diagonal is 20 cms. (10*2)

Let A be the area of rhombus. Therefore the area of rhombus is

A =  1/2*(product of diagonals)

A = 1/2*(20*48)

Therefore the Area of Rhombus is 480 sq.cm.

In this way we can find area of rhombus.

If you still have any queries feel free to ask in the comment section down below.

Related Questions

Woxsen University B.Sc. Admis...
Apply
Build Your Own Degree - Choose any 3 out of 8 Electives | 100% Plcament track | 100+ Global Partners | 200+ Industry Interactions
Symbiosis School for Liberal ...
Apply
Admissions open for BA/BSc. Liberal Arts (Honours) & BA / BSc. Liberal Arts (Honors) with Research
UPES B.Sc Admissions 2025
Apply
Ranked #46 amongst Universities in India by NIRF | Ranked #1 in Academic Reputation in India by QS World University Rankings
JSS University Noida Admissio...
Apply
170+ Recruiters Including Samsung, Zomato, LG, Adobe and many more | Highest CTC 47 LPA
GMAT™ Exam
Apply
Select test center appointment | Scores valid for 5 Years | Multiple Attempts | Round 2 Closing Soon
MATS University M.sc Admissio...
Apply
Approved by UGC | Merit-based scholarships
View All Application Forms

Download the Careers360 App on your Android phone

Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile

150M+ Students
30,000+ Colleges
500+ Exams
1500+ E-books