If the perimeter of an equilateral triangle is 360 cm. Then its area w

1.	If the perimeter of an equilateral triangle is 360 cm. Then its area will be
Answer» ${\orange{\underline{\underline{\red{\textsf{\textbf{Answer : }}}}}}}$ ➡ Area of the equilateral ∆ is 3600√3 cm. ${\orange{\underline{\underline{\red{\textsf{\textbf{Explanation : }}}}}}}$ GIVEN that, Perimeter of an equilateral ∆ is 360cm. We need to find the area, ${{\underline{\underline{{\textsf{\textbf{Concept : }}}}}}}$ Here, perimeter is given and needed to find the area. So, we EQUATE the perimeter to find each side and then USING the formula we'll find the area. We KNOW that, Perimeter of an equilateral ∆ = 3a ${ \boxed{ \rm \: Note : 3a \to \: Three \: equal \: sides}}$ Procedure : ⇒ 360 = 3a ⇒ $\rm \cancel{\frac{360}{3}} \\$ = a ⇒ 120 = a Therefore, Each side is 120cm. Using the formula : Area of an equilateral ∆ = $\rm \frac{\sqrt{3}}{4} a² \\ \sf$ ➡ Area = $\rm \frac{\sqrt{3}}{4}(120)²\\ \sf$ ➡ Area = $\rm \frac{\sqrt{3}}{\cancel4} × \cancel{120} × 120$ ➡ Area = $\rm \sqrt{3}× 30 × 120$ ➡ Area = $\rm 3600 \sqrt{3}cm.$ ${\pink{\underline{\underline{\purple{\textsf{\textbf{Hence, Area of the equilateral ∆ is 3600√3cm. }}}}}}}$