The sides of the triangular plot are $50$m, $30$m, and $40$m. Let $a=30$, $b=40$, $c=50$. We check if it's a right-angled triangle: $a^2 + b^2 = 30^2 + 40^2 = 900 + 1600 = 2500$. Also, $c^2 = 50^2 = 2500$. Since $a^2 + b^2 = c^2$, it is a right-angled triangle. The area of a right-angled triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. So, Area $= \frac{1}{2} \times 30 \times 40 = \frac{1}{2} \times 1200 = 600$ sq.m. To convert to 'Are', we use the conversion $1$ Are $= 100$ sq.m. So, $600$ sq.m. $= \frac{600}{100}$ Are $= 6$ Are.