A traffic signal board,indicating 'SCHOOL AHE | vedclass

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(D) For an equilateral triangle with side $a$,the area is given by $\frac{\sqrt{3}}{4} a^2$.Given that the perimeter of the equilateral triangle is $1

Vedclass · Accepted Answer

$900 \sqrt{3} \, cm^2$

Vedclass · Answer

(D) For an equilateral triangle with side $a$,the area is given by $\frac{\sqrt{3}}{4} a^2$.Given that the perimeter of the equilateral triangle is $180 \, cm$.Since all three sides are equal,$3a = 180 \, cm$,which gives $a = 60 \, cm$.Using Heron's formula,the semi-perimeter $s = \frac{	ext{Perimeter}}{2} = \frac{180}{2} = 90 \, cm$.The area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$.Substituting the values: $	ext{Area} = \sqrt{90(90-60)(90-60)(90-60)} \, cm^2$.$	ext{Area} = \sqrt{90 	imes 30 	imes 30 	imes 30} \, cm^2$.$	ext{Area} = \sqrt{3 	imes 30 	imes 30 	imes 30 	imes 30} \, cm^2$.$	ext{Area} = \sqrt{3 	imes (30)^2 	imes (30)^2} \, cm^2$.$	ext{Area} = 30 	imes 30 	imes \sqrt{3} \, cm^2 = 900 \sqrt{3} \, cm^2$.

$A$ 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 its perimeter is $180 \, cm$,what will be the area of the signal board?

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