Question

if the perimeter of rombus is 20cm and one of the daigonal os 8 cm the area of rombus is​

Answer 1

Given :

• Perimeter of Rhombus is 20 cm.
• Diagonal of Rhombus is 8 cm.

To Find :

• Area of the Rhombus.

Solution :

$\longmapsto\tt{Perimeter=20cm}$

$\longmapsto\tt{Diagonal\:{d}_{1}=8\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Perimeter\:of\:Rhombus=\dfrac{a+b}{2}}$

Putting Values :

$\longmapsto\tt{20=\dfrac{8+b}{2}}$

$\longmapsto\tt{20\times{2}=8+b}$

$\longmapsto\tt{40=8+b}$

$\longmapsto\tt{40-8=b}$

$\longmapsto\tt\bf{b=32}$

The Length of other Diagonal is 32 cm..

Now ,

$\longmapsto\tt{{d}_{1}=8\:cm}$

$\longmapsto\tt{{d}_{2}=32\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rhombus=\dfrac{1}{2}\times{d}_{1}\times{d}_{2}}$

Putting Values :

$\longmapsto\tt{\dfrac{1}{{\cancel{2}}}\times{{\cancel{8}}}\times{32}}$

$\longmapsto\tt{4\times{32}}$

$\longmapsto\tt\bf{128{cm}^{2}}$

So , The Area of Rhombus is 128 cm²..