Question

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Answer 1

Given, side of a
signal whose shape is an equilateral triangle= a

Semi perimeter, s=a+a+a/2=
3a/2

Using heron’s
formula,

Area of the signal board = √s (s-a) (s-b) (s-c)


= √(3a/2) (3a/2 – a) (3a/2 – a) (3a/2 –
a)



= √3a/2 × a/2 × a/2 × a/2



= √3a⁴/16

= √3a²/4

Hence, area of signal board with
side a by using Herons formula is= √3a²/4

 

Now,

Perimeter of an equilateral
triangle= 3a



Perimeter of the traffic signal board = 180 cm  (given)


 3a = 180 cm

 a = 180/3= 60 cm

Now , area of
signal board=√3a²/4



= √3/4 × 60 × 60

= 900√3 cm²

Hence , the area
of the signal board when perimeter is 180 cm is 900√3 cm².