Question

Find the area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m.

Answer 1

Perimeter of a rhombus = 80 m (given) 

We know, Perimeter of a rhombus = 4 x side

Let a be the side of a rhombus. 

4 x a = 80 

or a = 20 

One of the diagonal, AC = 24 m (given) 

Therefore OA = 1/2 x AC 

OA = 12 

In △AOB, 

Using Pythagoras theorem: 

OB² = AB² − OA² 

= 20² −12² 

= 400 – 144 

= 256 

or OB = 16 

Since diagonal of rhombus bisect each other at 90 degrees. 

And OB = OD 

Therefore, BD = 2 OB = 2 x 16 = 32 m 

Area of rhombus = 1/2 x BD x AC 

= 1/2 x 32 x 24

= 384 

Area of rhombus = 384 m².