To calculate the area of a right-angled triangle, you can use the formula:

A right-angled triangle is characterized by one angle that measures exactly $90$ degrees, indicating that the two sides forming this right angle are perpendicular to one another. These sides are designated as the base and height of the triangle. The area of a triangle is generally expressed by the formula above, which is particularly simple for right-angled triangles since the base and height correspond to the two sides that intersect at the right angle.

For instance, consider a right-angled triangle with a base of $5 \, \text{cm}$ and a height of $3 \, \text{cm}$. You can substitute these values into the formula to determine the area:

It is crucial to ensure that the base and height are perpendicular to each other, which is always the case in a right-angled triangle. If you mistakenly use the hypotenuse (the side opposite the right angle) as either the base or the height, the area calculation will be incorrect. The hypotenuse is not included in the area formula for right-angled triangles.

Keep in mind that the units of the area will be expressed in square units, such as square centimeters ($\text{cm}^2$) or square meters ($\text{m}^2$), depending on the units used for the base and height. This method provides a quick and reliable way to find the area of any right-angled triangle you may encounter.