Question

if the perimeter of a rhombus is 40cm and length of one of the diagonals is 12cm, what is the area of the rhombus?​

Answer 1

Answer:

Given the perimeter of rhombus is 40 cm and one diagonal is 12 cm

We know that perimeter of rhombus=2

p

2

+q

2

where -p and q are diagonal of rhombus

∴40=2

(12)

2

+q

2

⇒20=

144+q

2

⇒400=144+q

2

⇒q

2

=400−144=256

⇒q=16 cm

Then length of second diagonal is 16 cm

Then area of rhombus=

2

p×q

=

2

12×16

=

2

192

=96Cm

2