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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,
\(\Rightarrow \)
18 + 10 + c = 42
\(\Rightarrow \)
28 + c = 42cm
\(\Rightarrow \)
c = 42 - 28 cm
\(\Rightarrow \) 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 = \(\sqrt{s(s - a)(s - b)(s - c)}\)])
= \(\sqrt{21 × 3 × 11 × 7}\)
= \(\sqrt{7 × 3 × 3 × 11 × 7}\)
= \(21\sqrt{11} {cm}^2\)