Question

1.) 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?
2. The triangular side walls of a flyover have been used for advertisements. The sides of
the walls are 122 m, 22 m and 120 m (see Fig. 12.9). The advertisements yield as
earning of Rs 5000 per m per year. A company hired one of its walls for 3 months. How
much rent did it pay?​

Answer 1

$heron \: formula = \sqrt{s(s - a)(s - b)(s - c)}$

S = semi peramiter

here peramiter = 180

hence, S = 180/2 = 90

here triangle is equivalent,

hence, side = 180 /3 = 60

cause of equivalent triangle,

a = b = c = 60

$area \: = \sqrt{90(90 - 60)(90 - 60)(90 - 60)}$

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

$= \sqrt{2 430 000}$

$= 900 \sqrt{3}$