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:

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Answer 2

Answer:

900√3 CM square

Step-by-step explanation:

as board is an equilateral triangle

and in equilateral triangle all sides are equal

side - a CM

perimeter - 180 CM

perimeter of equilateral triangle = 3 x side

180 = 3 x a

180/3 = a

60 CM = a

semi perimeter = 180/2

= 90

area of signal board by heron 's formula ;

= √ s x (s-a) x (s-b) x (s-c)

= √ 90 x (90-60) x (90-60) x (90-60)

= √ 90 x 30 x 30 x 30

= √ 9 x 10 x 3 x 10 x 30 x 30

= √ 3 x 3 x 3 x 10 x 10 x 30 x 30

= 3 x 30 x 10 √ 3

= 900√3 cm square

hope it helps you