A field is shaped like an equilateral triangl | vedclass

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(A) For an equilateral triangle with side length $a = 120 \, m$,the semi-perimeter $s$ is calculated as:$s = \frac{a + a + a}{2} = \frac{3a}{2} = \fra

Vedclass · Accepted Answer

$3600 \sqrt{3} \, m^2$

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(A) For an equilateral triangle with side length $a = 120 \, m$,the semi-perimeter $s$ is calculated as:$s = \frac{a + a + a}{2} = \frac{3a}{2} = \frac{3 	imes 120}{2} = 180 \, m$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.Since $a = b = c = 120 \, m$,we have:Area $= \sqrt{180(180-120)(180-120)(180-120)}$Area $= \sqrt{180 	imes 60 	imes 60 	imes 60}$Area $= \sqrt{180 	imes 60^3} = \sqrt{3 	imes 60 	imes 60^3} = \sqrt{3 	imes 60^4}$Area $= 60^2 \sqrt{3} = 3600 \sqrt{3} \, m^2$.

$A$ field is shaped like an equilateral triangle. Its length is $120 \, m$ on each side. Calculate its area using Heron's formula.

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