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 it's perimeter is 180 cm ,what will be the area of the signal board?​

Answer 1

Step-by-step explanation:

side= a

perimeter=3a

= 180

=> a= 180/3= 60

a=b=c=60

=>s= (a+b+c) /2

=( 60+60+60)/2

=180/2

=90

$area = \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{90 \times (90 - 60)(90 - 60)(90 - 60)}$

$= \sqrt{90 \times 30 \times 30 \times 30}$

$= 30 \times 30 \sqrt{3}$

$= 900 \sqrt{3} sq \: cm$

Answer 2

Answer:

$perimeter - 180 ^. \\ p = a + b + c \\ 180 = a + a + a \\ a = 3a \: \\ a = \frac{180}{3} = 60cm \\ area \: of \: equilateral \: triangle = \frac{ \sqrt{3} }{4} \times {a}^{2} \\ 60 \times 60 \times \frac{ \sqrt{3} }{4} = 900 \sqrt{3}cm \: { \pink}\underline {ans}$

Step-by-step explanation:

$\huge \mathfrak \red{thanks \: dear} \star$