A traffic signal board, indicating 'SCHOOL AHEAD, is an equilateral mange
side 'o'. Find the area of the signal board, using Heron's formula If ite peame
180 cm, what will be the arep of the signal board!
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Step-by-step explanation:
let sides of the ∆ be 'a'
s =3a/2
A = √[(s)(s-a)(a-b)(s-c)]
A = √[ (3a/2)(3a/2 - a)(3a/2-a)(3a/2-a) ]
A = √[ (3a/2) (a/2)(a/2)(a/2) ]
A = √(3a⁴/16)
A = a²/4 × 3
A = 3/4a² is the formula of area of equilateral triangle
now, p = 180 cm therefore a = 180/3 = 60 cm
A = 3/4a²
=> A = 3/4 × 60²
=> A = 3/4 × 3600
=> A = 2700 cm²
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