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?

Solution

'a' = a
'b' = a
'c' = a
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Area of the signal board
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Perimeter = 180 cm
$rightwards double arrow$ 'a' + 'b' + 'c' = 180
$rightwards double arrow$ a + a + a = 180
$rightwards double arrow$ 3a = 180
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$rightwards double arrow space space space$ a = 60 cm
$therefore$ Area of the signal board $equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared$
$equals fraction numerator square root of 3 over denominator 4 end fraction left parenthesis 60 right parenthesis squared equals 900 square root of 3 space cm squared$
Alternatively,
$space space space space space straight s space equals fraction numerator 3 straight a over denominator 2 end fraction equals 3 over 2 left parenthesis 60 right parenthesis equals 90 space cm$
Area of the signal board
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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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