Question

a traffic signal board indicating school ahead is an equilateral triangle with side a find the area of the sign board using harrier heroines formula if its perimeter is 180 cm what will be the area of signal board​

Answer 1

Answer:

a+b+c=180

a=b=c (given)

Step-by-step explanation:

a+a+a=180

3a=180

a=60

s=a+b+c/2

180/2

=90

herons formula = √s(s-a)(s-b)(s-c)

√90(90-60)(90-60)(90-60)

√90(30)(30)(30)

√90×27000

√2430000

1558

Answer 2

Answer:

The area of this board is 0.15588 square decimetres. I know that the NCERT gives some other answer but the answer given by NCERT is just a simplified equivalent of this.

Step-by-step explanation:

$a=\frac{180}{3}$

$a=60cm$

$b=\frac{180}{3}$

$b=60cm$

$c=\frac{180}{3}$

$c=60cm$

$s=\frac{a+b+c}{2}$

$s=\frac{180}{2}$

$s=90cm$

By Heron's Formula:

Area of the =$\sqrt{s(s-a)(s-b)(s-c)}$

Area of the =$\sqrt{90(90-60)(90-60)(90-60)}$

Area of the =$\sqrt{90*30*30*30}$

Area of the =$\sqrt{2430000}$

Area of the =$1558.8{cm}^2$

Area of the =$0.15588{dm}^2$