Question

find the area of rhombus whose perimeter is 80m and one of whose diagonal is 24cm

Answer 1

The perimeter = 80m
each side =80/4 =20
the area= 200 x 24
= 480cm^2

Answer 2

Heya !!

Let ABCD is a rhombus , in which AD and BC are its two diagonals.

AB = AC = BD = CD.

Perimeter of rhombus ABCD = 80 cm.

4 × Side = 80

Side = 80/4

Side = 20 cm.

Let AD = 24 cm.

Therefore,

OA = 1/2 × AD = 1/2 × 24 = 12 cm.

And,

AB = 20 cm.

In right angled triangle OAB.

OB² = (20)² - (12)²

OB² = 400 - 144

OB = √256 = 16 cm.

Therefore,

BC = 2 × OB = 2 × 16 = 32 cm.

We know that,

Area of the rhombus = 1/2 × ( Product of its two diagonals )

=> 1/2 × ( 32 × 24 )

=> 768/2

=> 384 cm²

Hence,

Area of rhombus ABCD = 384 cm².