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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?
Asked by Rajmohan Last Modified
Answer read less
Gautam Pal
Maths Teacher for classes 6th to 10th with 6 years experience and having my own YouTube Channel for clearing doubts
Equilateral triangle of side 'a'.
So, s=(a+a+a)/2=3a/2.
So, Area of the triangle =√(3a/2) (3a/2 - a) (3a/2 - a) (3a/2 - a) = √(3a/2) (a/2) (a/2) (a/2) = (a²√3)/4.
Now, perimeter of the signal board = 180cm. Since, it is an equilateral triangle, each side will be 60cm. So, here a = 60cm and the area of the signal board can be found out by substituting the value of a = 60cm in the formula (a²√3)/4. So, it becomes, (60²√3)/4 = 1558.85cm²
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Given parameter =180 cm
i.e. 3a=180cm
a=60cm
S= perimeter /2 =90 cm
Heron formula is-
Area= [S{(S-a)+(S-b)+(S-c)}]^1/2
Where a ,b,c = side of the triangle
Here given triangle is equilateral
Therefore
a=b= c= 60cm
Now,
Area=[90{(90-60)+(90-60)+(90-60)}]^1/2
= [90{30+30+30}]^1/2
= [90×90]^1/2
= [90^2]^1/2=90cm sq.
Therefore are of the sign board =90cm sq
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Perimeter =180 so each side =60,then semi perimeter =90;
now by heron's formula = (90-60)(90-60)(90-60)=
*30*30*30
=3*3*100root3=900root3 squarecm
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