The area of a triangle, the length of whose sides are $50\text{ m}$, $78\text{ m}$ and $112\text{ m}$, is

We can find the area of the triangle using Heron's formula. Let the sides be $a=50\text{ m}$, $b=78\text{ m}$, and $c=112\text{ m}$.
First, calculate the semi-perimeter ($s$):

$$s=\frac{a+b+c}{2}=\frac{50+78+112}{2}=\frac{240}{2}=120\text{ m}$$

Now apply Heron's Area formula:

$$\text{Area}=\sqrt{s(s-a)(s-b)(s-c)}$$

$$\text{Area}=\sqrt{120\times (120-50)\times (120-78)\times (120-112)}$$

$$\text{Area}=\sqrt{120\times 70\times 42\times 8}$$

$$\text{Area}=\sqrt{2,822,400}=1680{\text{ m}}^2$$