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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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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