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

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#### Solution

Given that,

Perimeter of rhombus = 80m

Perimeter of rhombus = 4 × side

⇒ 4a = 80

⇒ a = 20m

Let AC = 24 m

∴ OA =`1/2AC=1/2xx24=12m`

In ΔAOB

`OB^2=AB^2-OA^2`

`⇒OB=sqrt(20^2-12^2)`

`sqrt(400-144)`

`sqrt(256)=16m`

Also BO = OD

[Diagonal of rhombus bisect each other at 90°]

∴ BD = 20B = 2 ×16 = 32 m

∴Area of rhombus = `1/2`×32×24=`384𝑚^2`

[∵Area of rhombus = 12×𝐵𝐷×𝐴𝐶]

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals

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