Question

if the perimeter of an equilateral triangle is 360 cm. Then its area will be​

Answer 1

${\orange{\underline{\underline{\red{\textsf{\textbf{Answer : }}}}}}}$

➡ 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 ∆ = $\rm \frac{\sqrt{3}}{4} a^2 \\ \sf$

➡ Area = $\rm \frac{\sqrt{3}}{4}(120)^2\\ \sf$

➡ Area = $\rm \frac{\sqrt{3}}{\cancel{4}} \times \cancel{120} \times 120$

➡ Area = $\rm \sqrt{3} \times 30 \times 120$

➡ Area = $\rm 3600 \sqrt{3} cm.$

Hence, Area of the equilateral triangle is 3600√3 cm.

Answer 2

Answer:

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{given}}}}}} \ast$

• The perimeter of an equilateral triangle = 360 cm

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{To \:find}}}}}} \ast$

• Area of the equilateral triangle=?

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{Formula}}}}}} \ast$

• $\bold \blue{ \: \: \: \: \: 3a \implies \: perimeter}$
• $\begin{gathered}\bold\rm\red \frac{\sqrt{3}}{4} a² \\ \sf\end{gathered}$

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{Diagram}}}}}} \ast$

$\setlength{ \unitlength}{1cm} \\ {picture}(0,0) \thicklines \qbezier(1,0)(1,0)(3,3) \qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{Concept}}}}}} \ast$

As provided in the given Question , First we will find the perimeter by 3a=> perimeter . In here it is 3a because as it is an equilateral triangle the sides are same ,(a) and the sides are three . So it is 3a.

Then we would find the area by the 2nd formula provided in the formula list.

$\huge \ast\bold { \underline{ \underbrace{ \underline {\textsf{ \green{Solution}}}}}} \ast$

⇒ 360 = 3a

⇒ a = 360/3

⇒ 120 = a

Using the 2nd formula :

$Area = \begin{gathered}\rm \frac{\sqrt{3}}{4}(120)²\\ \sf \end{gathered}$

$Area = \rm \frac{\sqrt{3}}{\cancel4} × \cancel{120}$

$Area = \rm \sqrt{3}× 30 × 120$

$Area = \rm 3600 \sqrt{3}cm.3600$