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.