What is the area (in m$$^2$$) of a triangular field whose sides measure 25 m, 39 m and 56 m?

We can obtain the area of the given triangle by Heron's formula.

semi perimeter = S = $$\frac{a+b+c}{2}$$

Where a = 25, b = 39, c = 56

So S = $$\frac{25+39+56}{2}$$

= $$\frac{120}{2}$$

= 60

area of a triangular field = $$\sqrt{S\left(S-a\right)\left(S-b\right)\left(S-c\right)\ }$$

= $$\sqrt{60\left(60-25\right)\left(60-39\right)\left(60-56\right)\ }$$

= $$\sqrt{60\times\ 35\times\ 21\times\ 4\ }$$

= $$\sqrt{176400}$$

= 420 m$$^2$$