In order to solve this exercise, you can use the Heron's formula for the area of a triangle:
[tex]A=\sqrt[]{p(p-a)(p-b)(p-c)}[/tex]
Where "a", "b" and "c" are the lengths of the sides of the triangle and "p" is half the perimeter.
The value of "p" can be found with this formula:
[tex]p=\frac{a+b+c}{2}[/tex]
Where "a", "b" and "c" are the lengths of the sides of the triangle.
In this case, you can set up that:
[tex]\begin{gathered} a=30\operatorname{cm} \\ b=35\operatorname{cm} \\ c=47\operatorname{cm} \end{gathered}[/tex]
Then, you can find "p":
[tex]\begin{gathered} p=\frac{30\operatorname{cm}+35\operatorname{cm}+47\operatorname{cm}}{2} \\ \\ p=56\operatorname{cm} \end{gathered}[/tex]
Then, substituting values into the Heron's formula and evaluating, you get:
[tex]\begin{gathered} A=\sqrt[]{(56cm)(56cm-30\operatorname{cm})(56cm-35\operatorname{cm})(56cm-47\operatorname{cm})} \\ A=\sqrt[]{275,154} \\ A\approx524.6\operatorname{cm}^2 \end{gathered}[/tex]
The answer is:
[tex]A\approx524.6\operatorname{cm}[/tex]
