A traffic signal board, indicating 'MEN AT WORK' is an equilateral triangle with side 'a'. Find the area of the signal board, using Heron's formula. If it's perimeter is 120cm, what will be the area of the signal board?
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Step-by-step explanation:
Given Perimeter =180 cm
Semi-perimeter s=
2
180
s=90 cm
Since all sides of equilateral triangle are equal
So,
Perimeter =180
a+a+a=180
3a=180
a=60 cm
Area of triangle =
s(s−a)(s−b)(s−c)
=
90(90−60)(90−60)(90−60)
=
90×30×30×30
=
(9×3×3×3)×(10)
4
=
(9
2
)×3×(10)
4
=9×
3
×(10)
2
=9×100×
3
=900
3
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