Question

The side of a rhombus is $26m$ and length of one of its diagonal is $20m$. The area of the rhombus is

• A. $120m^2$
• B. $240m^2$
• C. $480m^2$
• D. None

Answer 1

Answer: (C)

$480m^2$

Side $=26m$
Length of diagonal $=20m$

$BO=OD=\frac{1}{2}BD=\frac{1}{2}\times 20=10m$
Here $AB=BC=CD=DA=26m$
$BO=OD=10m$
In $\Delta AOD;A{D}^2=A{O}^2+O{D}^2$
$A{O}^2=A{D}^2-O{D}^2={26}^2-{10}^2$
$=676-100=567$
$AO=\sqrt{576}=24m$
Area of rhombus $=4\times$ Area of $\Delta AOD$
$=4\times \frac{1}{2}\times 10\times 24$
$=480m^2$