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Answer :
We know that an equilateral triangle has equal sides.
So, all sides are equal to a.
If Perimeter of triangle = 180 cm (Given)
\(\Rightarrow \) a + a + a = 180
\(\Rightarrow \) 3a = 180
\(\Rightarrow \) a = 60cm
\(\therefore \) \(s = \frac{a + a + a}{2}\)
(Since, 2s = a + b + c)
\(\Rightarrow \) \(s = \frac{3a}{2} = \frac{180}{2}\)
\(\Rightarrow \) s = 90cm
We also, know that, Area of an equilateral triangle
= \(\sqrt{s(s - a)(s - a)(s - a)}\)
(Since, Heron's formula = \(\sqrt{s(s - a)(s - b)(s - c)}\))
\(\Rightarrow \) Area
= \(\sqrt{90(90 - 60)(90 - 60)(90 - 60)}\)
= \(\sqrt{90 × 30 × 30 × 30}\)
= \(30 × 30\sqrt{3}\)
\(\Rightarrow \)Area of an equilateral triangle = \(900\sqrt{3} {cm}^2\))