Question

find the area of rhombus,whose perimeter is 80 cm.And length of one of its diagonal is 24cm.

find the area of rhombus
using herons formula​

Answer 1

Answer:

Here,s the answer :

Step-by-step explanation:

Let the side of rhombus be s cm.

so, 4s = 80

s = 20 cm.

now, 1st diagonal is 24 cm.

1/2 of 1st diagonal is 12 cm.

now, we know diagonals of a rhombus bisect each other at 90 degrees.

so, 20^2 - 12^2 = a^2 (Pythagorus' theorem)

or, 400 - 144 = a^2

or, 256 = a^2

or, a = 16 cm.

now, second diagonal is 32 cm.

z = (20 + 12 + 16) / 2 cm.

= 24 cm.

so area of rhombus = 4 * sq. root (24 * 4 * 12 * 8)

= 4 * 8 * 3 * 4 cm^2

= 32 * 24 cm^2

= 768 cm^2