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 its perimeter is
180 cm, what will be the area of the signal board?​

Answer 1

Answer:-    900√3

Step-by-step explanation:-

 Given Perimeter =180 cm

Semi-perimeter s =  180/2

s=90 cm

∵ All sides of equilateral triangle are equal

So, Perimeter =180

a+a+a=180

3a=180

a=60 cm

Area of triangle = √s(s-a)(s-b)(s-c)

= √90(90−60)(90−60)(90−60)

= √90×30×30×30

=√(9×3×3×3)×(10)²×²

= (9²)×3×(10)²×²

=9×√3 ×(10)²

=9×100×√3

=900√3

∴The area of the signal board will be 900√3

❤I HOPE IT REALLY HELPS YOU❤

Answer 2

Answer:

S=a+b+c /2

S=a+a+a /2

S=3a /2

Area of triangle= √S(S-a)(S-b)(S-c)

= √3a/2 (3a/2-a/1) (3a/2-a/1) (3a/2-a/1)

=√3a/2 (3a-2a/2) (3a-2a/2) (3a-2a/2)

=√3a/2 * a/2 * a/2 * a/2

=√3a⁴/16

=√3a² * a²/4

=√3a²/4

Perimeter = 180cm

3a=180

a=180/3

a=60cm

Area of signal board =√3/4 * a²

=√3/4 * (60) ²

=√3/4 * 3600

=900√3 cm² Ans.

Hope it helps.