Question

the perimeter of an equilateral triangle is 60m what will be its area​

Answer 1

Given :-

• Shape = Equilateral Triangle
• Perimeter = 60cm

To Find :-

• Area of the Equilateral Triangle

Solution :-

➞ Perimeter of equilateral triangle =3 × side

➞ 60 = 3 × side

➞ 60 ÷ 3 = side

➞ 20cm = side

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➞ Area of equilateral triangle = √3/4 × (Side)²

➞ Area = √3/4 × (20)²

➞ Area = √3/4 × 20 × 20

➞ Area = √3 × 5 × 20

➞ Area = √3 × 100

➞ Area = 173.20cm²

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Therefore, Area of equilateral triangle = 173.20cm²

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Answer 2

$\huge\bold{\underline{\underline{\sf{\red{Answer}}}}}:$

Given :

• Perimeter of an equilateral triangle is 60m

To Find :

• Area of an equilateral triangle

Solution :

Let's find out a side of an equilateral triangle

$\boxed{\sf{\pink{Perimeter _{(equilateral \: triangle)} =3 × side}}}$

By substituting values we get,

$\begin{gathered}\implies\sf 3 × side = 60m \end{gathered}$

$\begin{gathered}\implies\sf side = \cancel{\frac{60}{3} } \end{gathered}$

$\begin{gathered}\implies\sf side = 20m \end{gathered}$

Hence, The side of an Equilateral triangle is 20m

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Now,

$\boxed{\sf{\pink{Area_{(equilateral \: triangle)} = \frac{ \sqrt{3} }{4} (side)^{2} }}}$

By substituting values according to the formula we get,

$\begin{gathered}\implies\ \frac{ \sqrt{3} }{4} {(20)}^{2} \end{gathered}$

$\begin{gathered}\implies\sf \frac{ \sqrt{3} }{\cancel{4}} (\cancel{400) } ^{100} \end{gathered}$

$\begin{gathered}\implies\ 100 \sqrt{3} \end{gathered}$

$\begin{gathered}\implies\ 100 \times 1.732 \: ( \sqrt{3} = 1.732) \end{gathered}$

$\begin{gathered}\implies\red\ 173.2 {m}^{2} \end{gathered}$

Hence, The Area of an Equilateral triangle is 173.2m²