Question

A traffic signal board , indicating ' SCHOOL AHEAD' , is an equilateral triangle with side 'A' . find the area of the signal board , using heron's formula . if it's perimeter is 180 cm. what will be the area of the signal board?

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Answer 1

→ Hey Mate,

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→ Given Question:-

.  A traffic signal board , indicating ' SCHOOL AHEAD' , is an equilateral      triangle with side 'A' . find the area of the signal board , using heron's formula . if it's perimeter is 180 cm. what will be the area of the signal board?

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→ To Find:-

    . Area of the signal Board?

   

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→ Formula Used:-

   . $\sqrt{s(s-a)(s-b)(s-c)}$

    .  $\frac{a +b+c}{2}$

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→ Name of the Formulas:-

  . Heron's Formula

   . Semi Perimeter Formula

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→ Solution:-

    →   Given,

    ⇒        .  each side of an equilateral triangle Δ is 'α'.

    ⇒        Then,

    ⇒  α + α + α = 180°

    ⇒  3α  = 180°

    ⇒   α = $\frac{180}{3}$

    ⇒   α   = 60cm

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→ Semi Perimeter:-

   ⇒ $\frac{180}{2}$

   ⇒ 90cm

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→ Area of a triangle:-

     ⇒ $\sqrt{s(s-a)(s-b)(s-c)}$

     ⇒ $\sqrt{90(90-60)(90-60)(90-60)}$

     ⇒  $\sqrt{90 X 30 X30 X 30}$

     ⇒  $30 \sqrt{90 X 30}$

     ⇒  $30 \sqrt{3 X 30 X 30}$

     ⇒  $30 X 30\sqrt{3}$

     ⇒  $900\sqrt{3} cm^2$

∴ The Area of the signal board is $900\sqrt{3} cm^2$.

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→ More Information:-

  . brainly.in/question/1426064

  . brainly.in/question/1475507

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