Question

The perimeter of the rhombus is 24 cm. The measure of its one diagonal is 8 cm .Find the area of rhombus.

Answer 1

Answer:

Area of rhombus =8√20 cm².

Step-by-step explanation:

Let x be the length of each side of a rhombus.

Perimeter=24 cm (given)

4x=perimeter

4x=24

x=6 cm

Now we have to find the length of another diagonal

Assume =d₂

x²=(d₁/2)²+(d₂/2)²

(6)²=(8/2)²+(d₂/2)²⇒36-16=(d₂/2)²⇒20=(d₂/2)²⇒d₂=2√20 cm

∴Area of rhombus =1/2 x 8 x 2√20

                               = 8√20 cm²