Question

The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm, Then the area of the rhombus is

• A. 1000 cm${}^2$
• B. 500 cm${}^2$
• C. 1200 cm${}^2$
• D. 600 cm${}^2$

Answer 1

Answer: (D)

600 cm${}^2$

Given that, perimeter of rhombus is $100cm$ and one diagonal $40cm$

Perimeter of rhombus=4$\times$side

So side$=25cm$

And we know that in a rhombus diagonal divides rhombus in two eauilateral triangle.

Area of one triangle:- s$=(25+25+40)/2=45$

So area=(s$\times$(s-a)$\times$ (s-b)$\times$(s-c))^1/2

= (45$\times$(45-40)$\times$(45-25)$\times$(45-25))^1/2

$=300c{m}^2$

So total area is 300$\times$2=600cm^2

Hence, this is the answer.