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:

hope it help you so have it

Answer 2

$\mathfrak{\huge{\blue{\underline{Given:-}}}}$

➤ Side of the signal board = a

➤ Perimeter of the signal board = 180 cm

$\mathfrak{\huge{\blue{\underline{To \: Find:-}}}}$

➤ The area of the signal board.

$\mathfrak{\huge{\blue{\underline{Solution:-}}}}$

Given that,

Side of the signal board = a

Perimeter of the signal board = 3a = 180 cm

∴ a = 60 cm

Semi perimeter of the signal board = 3a/2

By using Heron’s formula,

Area of the triangular signal board will be,

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

$\sf \longrightarrow \sqrt{(3a/2)(3a/2-a)(3a/2-a)(3a/2-a)}$

$\sf \longrightarrow \sqrt{3a/2 \times a/2 \times a/2 \times a/2}$

$\sf \longrightarrow \sqrt{3a^{4}/16}$

$\sf \longrightarrow \sqrt{3} a^{2}/4$

$\sf \longrightarrow \sqrt{3}/4 \times 60 \times 60= \underline{\underline{900 \sqrt{3} \: cm^{2}}}$