Math, asked by xMrUnknownx, 10 months ago

In an equilateral triangle perimeter is 12 cm Find its area

Answers

Answered by nisha382
40

Answer:

Hello mate ❤️

We know that ,

each side if a equilateral triangle is equal

let,each side be x

according to the Q,

x+x+x=12

=>3x=12

=>x=4[dividing by 3]

•°•area of the triangle=√3/4 x^2

=√3/4×16

=16√3/4

=4√3cm^2

•°•Area of the triangle is 4√3cm^2

FORMULA:-

  • Area of equilateral triangle=√3/4×(side)^2

Hope this help u

Answered by Anonymous
11

\huge\mathfrak\blue{Answer:}

Given:

  • We have been an equilateral Triangle whose perimeter is 12 cm

To Find:

  • We have to find the area of Triangle

Solution:

Let the side of Triangle be = a

According to the Question

\longrightarrow \sf{Perimeter \: of \: Triangle = 12 cm}

\longrightarrow \sf{ a + a + a = 12 }

\longrightarrow \sf{ 3a = 12 }

\longrightarrow \sf{ a = \dfrac{12}{3} }

\longrightarrow \sf{ a = \dfrac{12}{3}}

\longrightarrow \sf{ a = 4 }

Hence \boxed{\sf{\orange{ Side \: of \: Triangle = 4 cm }}}

________________________________

Finding the area of Given Triangle

\longrightarrow \sf{ Area = \dfrac{\sqrt{3}}{4} \times {(a)}^{2}}

\longrightarrow \sf{ Area = \dfrac{\sqrt{3}}{4} \times {(4)}^{2}}

\longrightarrow \sf{ Area = \dfrac{\sqrt{3}}{4} \times (16)}

\longrightarrow \sf{ Area = 4 \sqrt{3} {cm}^{2}}

Hence \boxed{\sf{\green{ \: Area \: of Triangle \: is = 4 \sqrt{3} {cm}^{2}}}}

____________________________

\sf{\blue{Hence \: Area \:  of \: Triangle \: is \: 4 \sqrt{3} {cm}^{2}}}

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