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.
To understand better, go through Class 9 maths NCERT solutions- Heron’s formula
Comments
Post a Comment
Thank you we will contact ASAP.