Ex 12.1, 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?
Area of triangle = √(s(s−a)(s−b)(s −c))
Here, s is the semi-perimeter,
and a, b, c are the sides of the triangle
Given Perimeter = 180 cm
Semi-Perimeter = s =Perimeter/2
s = 180/2
s = 90 cm
Given that the triangle is equilateral
Since all sides of equilateral triangle are equal
∴ a = b = c
Perimeter = 180 cm
a + a + a = 180 cm
3a = 180 cm
a = 180/3 cm
a = 60 cm
Area of triangle = √(s(s−a)(s−b)(s −c))
Putting a = b = c = 60 cm , s = 90 cm
Area of signal board = √(90(90−60)(90−60)(90 −60))
= √( 90(30)(30)(30) )
= √( (9×3×3×3)×(10)4)
= √((9×9)×3×(10)4)
= √((92)×3×(10)4)
= √92×√3 × √((10)4)
= 9×√3 ×(〖104)〗^(1/2)
= 9 ×√3 × (102)
= 9 × 100 × √3
= 900√3
Thus, Area = 900√3 cm2

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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