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Class 9 maths NCERT solutions- Heron’s formula

Class 9 maths NCERT solutions-Chapter 12 Heron’s formula

To understand this formula better let us go through Class 9 Maths solutions

 Area of a triangle=√s(s-a)(s-b)(s-c)
Exercise 1
Question 1.A traffic signal board, indicating ‘SCHOOL AHEAD’ is an equilateral triangle with side   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? MATHS Question
Solution:-Perimeter=sum of all sides
= 180=3a
=side of a triangle 180/3=60cm
=s=180/2=90
= using herons formula =√s (s-a)(s-b)(s-c)
=√90(90-60)(90-60)(90-60)
=√90*30*30*30
=√3*3*10*3*10*3*10*3*10
=3*3*10*10√3
=900√3cm²
Question – Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area?
Solution- Let the ratio b x
Perimeter= sum of all sides
540 =12x+17x+25x
540=54x
X=540/54=10
Side a =12*10=120
Side b=17*10=170
Side c=25*10=250
S=a+b+c/2=540/2=270 cm
Area of a triangle using herons formula =√s(s-a)(s-b)(s-c)
=√270 (270-120)(270-170)(270-250)
=√270*150*100*20
=√3*3*3*10*3*5*10*10*10*10*2
=√3*3*3*3*2*5*10*1010*10*10*2*5
=√3*3*3*3*2*2*5*5*10*10*10*10
=3*3*2*5*10*10
=9000 cm²
Application of Herons Formula in finding an area in quadrilaterals
Using the Heron’s formula, we can calculate an area of a quadrilateral whose sides and one diagonal is given by dividing the quadrilateral into two triangles.

For more solutions and last year papers, click on Class 9 NCERT solutions or CBSE question paper for Class 9. It will enable you to review the complete subject matter for Class 9 designed by the experts.

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