Question

traffic signal board, indicating 'SCHOOLAHEAD', is an equilateral triangle with side 'a'.

Find the area of the signal board, using Heron's Formula. If its perimeter is 180 cm,​

Answer 1

Answer:

Given Perimeter =180 cm

Semi-perimeter s=

2

180

s=90 cm

Since 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)

4

=

(9

2

)×3×(10)

4

=9×

3

×(10)

2

=9×100×

3

=900

3