Question

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 it’s perimeter is 180cm, what will be the area of the signal board ?

Answer 1

Answer:

Step-by-step explanation:

side = a

semiperimeter = 3a/2

area = $\sqrt{s(s-a)(s-b)(s-c)}$

= $\sqrt{(3a/2)*(3a/2 - a)^3}$

= $\sqrt{(3a/2)*(a/2)^3}$

= $\sqrt{3a^4/16}$

= $\sqrt{3}a^2/4$

if perimeter = 180cm, a = 60cm

area = $\sqrt{3} * 3600/4$

$=900\sqrt{3} cm^2$

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