Imagine cutting a rectangular tabletop diagonally from corner to corner to create two identical right-angled triangle pieces; the area of one piece is half the product of its two perpendicular sides.

Remember the fundamental Pythagorean triples such as $3:4:5$, which can be scaled up by a factor of 4 to quickly identify the sides as $12:16:20$.

According to Pythagoras' theorem, the square of the hypotenuse ($h$) equals the sum of the squares of the base ($b$) and perpendicular ($p$), expressed as $b^2 + p^2 = h^2$. Substituting the given values ($12^2 + p^2 = 20^2$), we find $p = \sqrt{400 - 144} = 16$ cm. The area is then computed using the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

Memorize common Pythagorean triples (e.g., 3-4-5, 5-12-13, 8-15-17) to drastically reduce calculation time in competitive exams.