#### Question

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

#### Solution

Perimeter of the rhombus = 100 cm

⇒ `4 xx` side = 100

⇒ side = `100/4` = 25cm

Thus, each side of the rhombus = 25 cm.

Diagonals of a rhombus bisect each other at 90°

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 diagnols) = `1/2 xx 14 xx 48` = 336 cm²

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Solution If Perimeter of a Rhombus is 100 Cm and Length of One Diagonal is 48 Cm, What is the Area of the Quadrilateral ? Concept: Area of a Rhombus.