Class 9 Maths Chapter 12 Heron’s Formula
Heron’s Formula is used to find the area of a triangle. It is an essential chapter in the sense that it can help you gain plenty of marks if you study it carefully. You can read this chapter from the study material provided by GharPeShiksha! This chapter has been explained excellently and in a step-by-step manner in the PDFs provided by GharPeShiksha. The PDFs also contain Revision Notes, NCERT solutions, NCERT Exemplar Solutions, Previous Year Questions of this Chapter, Formulae Sheet, Model Answer Sheets designed by expert teachers. The study material is revised each year as per the syllabus requirements and is consistent with the new exam pattern. It has a lot of practice questions for the students to enhance their understanding. You can avail of it through the website of GharPeShiksha only.
What is a triangle?
The plane closed figure, with three sides and three angles is called as a triangle.
Types of Triangles (Based on the sides)
- Equilateral triangle
- Isosceles triangle
- Scalene triangle
Types of Triangles (Based on the sides)
- Acute angled triangle
- Obtuse angled triangle
- Right angled triangle
AREA OF TRIANGLE
Area of triangle or right angle triangle= ½baseheight
Area of equilateral triangle = √3a2/4
Area of isosceles triangle= (1/4) × b × √ (4a2 – b2)
AREA OF TRIANGLE BY HERON’S FORMULA
Area = √[s(s – a)(s – b)(s – c)]
Where s= (a+b+c)/2
Example– A triangle PQR has sides 4 cm, 13 cm and 15 cm. Find the area of the triangle.
Semi perimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16 cm
By heron’s formula,
A = √[s(s-a)(s-b)(s-c)]
Hence, A = √[16(16-4)(16-13)(16-15)] = √(16 x 12 x 3 x 1) = √576 = 24 sq.cm
Example–
The sides of triangle are a, a, a units
s=(a+ a+ a)/2=3a/2
Using Heron’s formula
Area of equilateral triangle is
HERON’S FORMULA FOR QUADRILATERAL
Let ABCD he a quadrilateral to find the area of a quadrilateral we need to divide the quadrilateral in triangular parts
Here AB||CD and AC & BD are the diagonals.
AC divides the quad ABCD into two triangles ADC and ABC.
Now we have two triangles here.
Area of quad ABCD = Area of ∆ADC + Area of ∆ABC (Calculate area of triangles by Heron’s formula)
