Question

traffic signal board indicating 'SCHOOL Ahead is an equilateral triangle with side 'a' .find area of signal board using herons formula . if it's perimeter 180cm what will be area of signal board

Answer 1

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Answer 2

$\huge\tt{\underline{\underline{Solution :-}}}$

Area of Signal board =

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

( equilateral ∆)

Therefore, In equilateral ∆

a = b= c = a

Perimeter of∆ = 180cm.

Perimeter of equilateral ∆ = 3 × side

180 cm = 3 × a

a = $\huge\sf\frac{180}{3}$

a = 60cm.

S = $\huge\sf\frac{p}{2}$ = $\huge\sf\frac{180}{2}$ = 90cm.

Area of equilateral triangle =

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

$\sf\sqrt{90(30)(30)(30)}$

$\sf\sqrt{3 × 30 × 30 × 30 × 30}$

$\sf{30 × 30}$ $\sf\sqrt{3}$

900 √3 cm^2.