We can use the Heron's Formula which is:
[tex]A= \sqrt{s(s-a)(s-b)(s-c)} [/tex]
where s is the semiperemeter (half the perimeter) and a,b, and c represent the length of the sides.
We first compute for s:
[tex]s= \frac{a+b+c}{2} = \frac{25+39+40}{2} = \frac{104}{2} =52[/tex]
So we plug in the given values to the formula:
[tex]A= \sqrt{52(52-25)(52-39)(52-40)} \\ = \sqrt{52(27)(13)(12)} \\ = \sqrt{13^2*2^4*3^4} \\ =13*2^2*3^2 \\ =468cm^2[/tex]
