The base of a right-angled triangle measures 48 cm and its hypotenuse measures 50 cm.

Let $\triangle P Q R$ be a right-angled triangle and $P Q \perp Q R$.

Now,

$P Q=\sqrt{P R^{2}-Q R^{2}}$

$=\sqrt{50^{2}-48^{2}}$

$=\sqrt{2500-2304}$

$=\sqrt{196}$

$=14 \mathrm{~cm}$

Area of triangle $=\frac{1}{2} \times Q R \times P Q$

$=\frac{1}{2} \times 48 \times 14$

$=336 \mathrm{~cm}^{2}$