Question

A traffic signal board including SCHOOL AHEAD is an equilateral triangle with side 'a'. Find the area of the signal board using heron's formula if its perimeter is 180cm. What will be the area of the signal board?

Answer 1

Solution:

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.