Question

If perimeter of a rhombus is 100 cm and length of one diagonal is 48 cm, what is the area of the quadrilateral?

Answer 1

Perimeter of the rhombus = 100 cm

⇒ `4  xx` side = 100

⇒ side = `100/4` = 25 cm 

Thus, each side of the rhombus = 25 cm.

Diagonals of a rhombus are perpandicular bisector of each other.

So, AO = OC = `48/2` = 24 cm

In Δ AOB,

We apply Pythagoras theorem,

AO² + OB² = AB²

⇒ 24²  + OB²  = 25² 

⇒ OB²  = 625 - 576 = 49

⇒ OB = 7 cm 

So, DB = `2 xx "OB" = 2 xx 7` = 14 cm

Area of rhombus = `1/2 xx` (product of diagonal)

= `1/2 xx 14 xx 48`

= 336 cm²