The perimeter of a rhombus is 148 cm, and one of its diagonals is 24 cm. The area (in cm² ) of the rhombus is:

840

We know that,

Perimeter of Rhombus = 4 × side

Area of Rhombus = \(\frac{1}{2}\) × d1 × d2

where, d1 and d2 are diagonals of rhombus

Perimeter = 4 × side

= 148 = 4 × side

= side = 37 cm

In triangle  ΔAOB,

= AB² = AO² + OB²

= (37)² = (12)² + OB²

= 1369 = 144 + OB²

= OB² = (1369 – 144)

= OB² = 1225 cm²

= OB = 35 cm

BD = 2 × OB = 2 × 35  = 70 cm

Area of Rhombus = \(\frac{1}{2}\) × 24 × 70 = 840 cm²