Question

a traffic signal board, indicating 'SCHOOL AHEAD' is an equilateral triangle with side'a'. find the area of the signal board, using Herons's formula. if it's perimeter is 180cm, what will be the area of the signal board.

Answer 1

this is the sum of it the lesson is herons formula

Answer 2

Answer:

900$\sqrt{3}$$cm^{2}$

Step-by-step Explanation:

method 1;

perimeter=180cm

3a=180cm

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

 = 60cm

since it is an equilateral triangle, a=b=c=60cm

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

=$\frac{180}{2}$

=90cm

area of the triangle=

$\sqrt{s(s-a)(s-b)(s-c)} \\=\sqrt{90(90-60)(90-60)(90-60)} \\=\sqrt{90(30)(30)(30)} \\=\sqrt{30x3x30x30x30} \\=30x30\sqrt{3} \\=90\sqrt{3} cm^{2}$

method 2;

$area of triangle=\sqrt{\frac{3}{4} } a^{2} sq.units\\ =\sqrt{\frac{3}{4} } x60x60cm^{2} \\ =900\sqrt{3} cm^{2}$