Question

The perimeter of an equilateral triangle is 3√3 cm. Find the area of the triangle​

Answer 1

GIVEN :-

• Perimeter of Equilateral triangle = 3√3 cm.

TO FIND :-

• The area of Equilateral triangle.

SOLUTION :-

As we know that, in Equilateral triangle all the sides are equal so,

⇒ Perimeter of Equilateral ∆ = 3√3

⇒ sum of all sides = 3√3

⇒ side + side + side = 3√3

⇒ 3side = 3√3

⇒ side = 3√3/3

⇒ side = √3 cm.

Now as we know that,

⇒ Area of Equilateral ∆ = √3/4 × (side)²

⇒ Area of Equilateral ∆ = √3/4 × (√3)²

⇒ Area of Equilateral ∆ = √3/4 × √9

⇒ Area of Equilateral ∆ = √3/4 × 3

⇒ Area of Equilateral ∆ = 3√3/4 cm²

Hence the area of the equilateral triangle is 3√3/4 cm².

Answer 2

$\underline{\frak{\qquad Given: \qquad}}$

• The perimeter of an equilateral triangle is 3√3 cm.

$\underline{\frak{\qquad To\:Find: \qquad}}$

• Area of traingle = ?

$\underline{\frak{\qquad Solution: \qquad}}$

$\qquad \quad\tiny{ \dag \: \: \underline{\sf First\:of\:all\:let's \: find \: the \: sides \: of \: equilateral \: \Delta : }}$

$:\implies \sf Perimeter \: of \: equilateral \: \Delta = 3a$

$:\implies \sf 3 \sqrt{3} = 3a$

$:\implies \sf \dfrac{3 \sqrt{3}}{3} = a$

$:\implies \sf \sqrt{3} = a$

$:\implies \underline{ \boxed{\sf a = \sqrt{3}\: cm}}$

$\therefore\:\underline{\textsf{Sides of equilateral \Delta is \textbf{ \sqrt{\text 3} cm}}}.$

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$\qquad \quad\tiny{ \dag \: \: \underline{\sf Now, let's \: find \: the \: area \: of \: equilateral \: \Delta : }}$

$\dashrightarrow\:\:\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{ \sqrt{3} }{4} \times {a}^{2}$

$\dashrightarrow\:\:\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{ \sqrt{3} }{4} \times { \left( \sqrt{3} \right)}^{2}$

$\dashrightarrow\:\:\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{ \sqrt{3} }{4} \times { \sqrt{9}}$

$\dashrightarrow\:\:\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{ \sqrt{3} }{4} \times { \sqrt{3 \times 3}}$

$\dashrightarrow\:\:\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{ \sqrt{3} }{4} \times 3$

$\dashrightarrow\:\:\underline{\boxed{\sf Area_{ \tiny(of \: equilateral \: \Delta)} = \dfrac{3 \sqrt{3} }{4} \: {cm}^{2}}}$

$\therefore\:\underline{\textsf{The area of equilateral \Delta is \textbf{ \dfrac{\text{3} \sqrt{3}}{ \text{4}} {cm} ^{ \text2} }}}.$

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