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

Base = 48 cm
Hypotenuse =50 cm
First we will find the height of the triangle; let the height be 'p'.

$\Rightarrow(\text { Hypotenuse })^{2}=(\text { base })^{2}+p^{2}$

$\Rightarrow 50^{2}=48^{2}+p^{2}$

$\Rightarrow p^{2}=50^{2}-48^{2}$

$\Rightarrow p^{2}=(50-48)(50+48)$

$\Rightarrow p^{2}=2 \times 98$

$\Rightarrow p^{2}=196$

$\Rightarrow p=14 \mathrm{~cm}$

Area of the triangle $=\frac{1}{2} \times$ base $\times$ height

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

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