One diagonal of a rhombus is $8\sqrt{3}$ cm . If the other diagonal is equal to its side, then the area (in cm²) of the rhombus is :

$32\sqrt{3}$

We know that,

The diagonals of a rhombus bisect each other at right angles.

Area of a rhombus = \(\frac{1}{2}\) × Diagonal₁ × Diagonal₂

Given,

D₁ =  8\(\sqrt {3}\) cm 

D₂ = side of the rhombus = a 

By Pythagoras theorem

a² = \(\frac{a^2}{4}\)+ (4\(\sqrt {3}\))²

= a² = 64 

= a = 8 cm = D₂

The area of the rhombus = \(\frac{1}{2}\) × 8 × 8\(\sqrt {3}\)=32\(\sqrt {3}\) cm²