Question

The area of an equilateral triangle having side length equal to 4cm is​

Answer 1

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

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

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• Length of sides of equilateral triangle is 4 cm

$\:\:$

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

$\:\:$

• Area of equilateral triangle

$\:\:$

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

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1st Method

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We know that ,

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

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

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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 = 4 cm

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⟮ Putting above value in ⓵ ⟯

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

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

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: ➜ $\sf \dfrac { \sqrt 3 } { 4 } \times 16$

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: ➜ $\sf \sqrt 3 \times 4$

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: : ➨ 6.92 sq. cm

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• Hence the area of equilateral triangle is 4√3 sq. cm. or 6.92 sq. cm

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2nd Method

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We know that ,

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

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$\sf \sqrt { s(s - a)(s - b)(s - c) }$ ⚊⚊⚊⚊ ⓶

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Where ,

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• a = First side

• b = Second side

• c = Third side

• s = Semi perimeter

• $\sf s = \dfrac { a + b + c } { 2 }$

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$\underline{ \underline{\bold{\texttt{For the given triangle :}}}}$

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As the given triangle is equilateral hence its all side are of same length i.e 4 cm

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• a = 4 cm

• b = 4 cm

• c = 4 cm

• $\sf s = \dfrac { 4 + 4 + 4} { 2 } = \dfrac { 12 } { 2 } = 6 \: cm$

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⟮ Putting the above values in ⓶ ⟯

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: ➜ $\sf \sqrt { s(s - a)(s - b)(s - c) }$

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: ➜ $\sf \sqrt { 6(6 - 4)(6 - 4)(6 - 4) }$

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: ➜ $\sf \sqrt { 6(2)(2)(2) }$

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: ➜ $\sf \sqrt { (2 \times 3)(2)(2)(2) }$

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: ➜ $\sf 2 \times 2\sqrt3$

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: ➜ $\sf 4\sqrt3$

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: : ➨ 6.92 sq.cm

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• Hence the area of equilateral triangle is 4√3 sq. cm. or 6.92 sq. cm

Answer 2

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

$\:\:$

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

$\:\:$

• Length of sides of equilateral triangle is 4 cm

$\:\:$

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

$\:\:$

• Area of equilateral triangle

$\:\:$

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

$\:\:$

We know that ,

$\:\:$

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

$\:\:$

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

$\:\:$

Where ,

$\:\:$

a = Side of triangle

$\:\:$

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

$\:\:$

a = 4 cm

$\:\:$

⟮ Putting above value in ⓵ ⟯

$\:\:$

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

$\:\:$

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

$\:\:$

: ➜ $\sf \dfrac { \sqrt 3 } { 4 } \times 16$

$\:\:$

: ➜ $\sf \sqrt 3 \times 4$

$\:\:$

: : ➨ 6.92 sq. cm

$\:\:$

• Hence the area of equilateral triangle is 4√3 sq. cm. or 6.92 sq. cm