In a rectangle, the angle between a diagonal and a side is 30°

(c) $16 \sqrt{3} \mathrm{~cm}^{2}$

Let $A B C D$ be the rectangle in which $\angle B A C=30^{\circ}$ and $A C=8 \mathrm{~cm}$.

In $\Delta B A C$, we have:

$\frac{A B}{A C}=\cos 30^{\circ}=\frac{\sqrt{3}}{2}$

$\Rightarrow \frac{A B}{8}=\frac{\sqrt{3}}{2}$

$\Rightarrow A B=8 \frac{\sqrt{3}}{2}=4 \sqrt{3} \mathrm{~m}$

Again,

$\frac{B C}{A C}=\sin 30^{\circ}=\frac{1}{2}$

$\Rightarrow \frac{B C}{8}=\frac{1}{2}$

$\Rightarrow B C=\frac{8}{2}=4 \mathrm{~m}$

$\therefore$ Area of the rectangle $=(A B \times B C)=(4 \sqrt{3} \times 4)=16 \sqrt{3} \mathrm{~cm}^{2}$