Question

find the area of Rhombus whose perimeter is 200 m and one of the diagonal is 80 metre​

Answer 1

SOLUTION:-

Given,

Perimeter of rhombus= 200m

We know that perimeter of rhombus;

=) 4× side

Therefore,

=) 4a=200

=) a= 200/4

=) a= 50

Let AC= 80m

So,

OA= 1/2AC = 1/2× 80 = 40m

In ∆AOB,

Using Pythagoras Theorem;

OB² = AB² - OA²

OB² = 80² - 40²

OB² = 6400 - 1600

OB² = 4800

OB = √4800

OB= 69.28

Also,

BO= OD

[diagonal of rhombus bisect each other at 90°]

=) BD = 2OB = 2×69.28 = 138.56m

We know that, area of rhombus;

=) 1/2 × BD × AC

=) 1/2 × 138.56 × 80

=) 138.56 × 40

=) 5542.4m²

Hope it helps ☺️