The diagonals of a rhombus are 18 cm and 24 cm. Find :

(i) its area

(ii) length of its sides

(iii) its perimeter

(i) Given:

The diagonals of a rhombus are 18 cm and 24 cm.

As we know, the area of rhombus = $\dfrac{1}{2}$ x product of its diagonal

= $\dfrac{1}{2}$ x 18 x 24 cm²

= $\dfrac{1}{2}$ x 432 cm²

= 216 cm²

Hence, the area of the rhombus is 216 cm².

(ii) AC = 18 cm

Then, OA = OC = $\dfrac{18}{2}$ = 9 cm

And, BD = 24 cm

Then, OB = OD = $\dfrac{24}{2}$ = 12 cm

Since the diagonals of a rhombus bisect at 90°.

Applying pythagoras theorem in triangle AOB, we get:

AB² = OA² + OB²

⇒ AB² = (9)² + (12)²

⇒ AB² = 81 + 144

⇒ AB² = 225

⇒ AB = $\sqrt{225}$

⇒ AB = 15 cm

Hence, the length of each side of the rhombus is 15 cm.

(iii) As we know, the perimeter of the rhombus = 4 x side

= 4 x 15 cm

= 60 cm

Hence, the perimeter of the rhombus is 60 cm.