Question

Find the area of equilateral triangle whose perimeter is 180 cm with explanation
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Answer 1

Given :

Perimeter of equilateral triangle = 180 cm

To find :

Area of triangle.

Solution :

Let the side of equilateral triangle be "a" cm.

∵ Perimeter of equilateral triangle = 3 * side

So atq,

⇒ 3a = 180

⇒ a = 180/3

⇒ a = 60 cm.

Now, area of equilateral Δ = √3/4 a²

∴ Area of equilateral Δ = √3/4 * (60)²

                                       = √3/4 * 3600

                                       = 1558.846 cm²

Therefore,

Area of equilateral triangle = 1558.846 cm²

Answer 2

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• Perimeter of equilateral triangle is 180 cm

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Area of equilateral triangle

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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We know that

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$\underline{ \underline{\bold{\texttt{Perimeter of equilateral triangle :}}}}$

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: ➜ P = 3a ⚊⚊⚊⚊ ⓶

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Where ,

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• P = Perimeter of equilateral triangle

• a = Side of equilateral triangle

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$\underline{ \underline{\bold{\texttt{Perimeter of given equilateral triangle :}}}}$

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• P = 180 cm

• a = a

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⟮ Putting the above values in ⓵ ⟯

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: ➜ P = 3a

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: ➜ 180 = 3a

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: ➜ $\sf a = \dfrac { 180 } { 3 }$

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: ➜ a = 60 cm

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• Hence the side of equilateral triangle is 60 cm

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━━━━━━━━━━━━━━━━━━━━━━━━━

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We know that ,

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$\underline{ \underline{\bold{\texttt{Area of equilateral triangle :}}}}$

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➠ $\bf \dfrac { \sqrt 3 } { 4 } \times a ^2$ ⚊⚊⚊⚊ ⓶

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Where ,

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• a = Side of triangle

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$\underline{ \underline{\bold{\texttt{Area of given equilateral triangle :}}}}$

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• a = 60 cm

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⟮ Putting above value in ⓶ ⟯

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: ➜ $\sf \dfrac { \sqrt 3 } { 4 } \times a ^2$

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: ➜ $\sf \dfrac { \sqrt 3 } { 4 } \times (60)^2$

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: ➜ $\sf \dfrac { \sqrt 3 } { 4 } \times 60 \times 60$

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: ➜ $\sf \sqrt 3 \times 15 \times 60$

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: ➜ $\sf \sqrt 3 \times 900$

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: : ➨ 1558.84 sq. cm

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• Hence the area of equilateral triangle is 900√3 sq. cm. or 1558.84 sq. cm