Answer :

Let the sides of a triangle a = 18 cm, b = 10 cm and c
We have, perimeter = 42 cm
So, a + b + c = 42
By substituting the values,
18 + 10 + c = 42
28 + c = 42cm
c = 42 - 28 cm
Thus, c = 14cm
Now, we know that, $s=\frac{a+b+c}{2}$
Therefore, $s=\frac{18+10+14}{2}=\frac{42}{2}=21cm$

Now, Area of triangle = $\sqrt{21(21?18)(21?10)(21?14)}$ ...(Since, Heron's formula [area = $\sqrt{s(s?a)(s?b)(s?c)}$])
= $\sqrt{21\times 3\times 11\times 7}$
= $\sqrt{7\times 3\times 3\times 11\times 7}$
= $21\sqrt{11}{cm}^2$