Question

a traffic signal board indicating 'SCHOOL AHEAD' IS AN EQILATERAL 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;

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.