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## CBSE Class 9 Maths Notes Chapter 7 Heron’s Formula

**Heron’s Formula Class 9 Notes Chapter 7**

1.** Triangle:** A plane figure bounded by three line segments is called a triangle.

In Î”ABC has

(i) three vertices, namely A, B and C.

(ii) three sides, namely AB, BC and CA.

(iii) three angles, namely âˆ A, âˆ B and âˆ C.

2. Types of Triangle on the Basis of Sides

(i) **Equilateral triangle:** A triangle having all sides equal is called an equilateral triangle.

In equilateral Î”ABC,

i.e., AB = BC = CA

(ii) **Isosceles triangle:** A triangle having two sides equal is called an isosceles triangle.

In isosceles Î”ABC,

i.e., AB = AC

(iii) **Scalene triangle:** A triangle in which all the sides are of different lengths is called a scalene triangle.

In scalene Î”ABC,

i.e., AB â‰ BC â‰ CA

3.** The perimeter of a Triangle:** The sum of the lengths of three sides of a triangle is called its perimeter.

Let, AB = c, BC = a, CA = b

i.e., Perimeter of Î”ABC, 2s = a + b + c

**Herons Formula Class 9 Notes Chapter 7**

4. **Area of a Triangle:** The measure of the surface enclosed by the boundary of the triangle is called its area.

Area of triangle = \(\frac { 1 }{ 2 }\) Ã— Base Ã— Height

Area of right angled triangle = \(\frac { 1 }{ 2 }\) Ã— Base Ã— Perpendicular

5. **Area of a Triangle (Heronâ€™s Formula):** If a triangle has a, b and c as sides, then the area of a triangle by Heronâ€™s formula = \(\sqrt { s\left( s-a \right) \left( s-b \right) \left( s-c \right) }\)

where, s (semi-perimeter) = \(\frac { a+b+c }{ 2 }\)

Note: This formula is highly applicable in the case when we don’t have the exact idea about height.

**Class 9 Herons Formula Notes Chapter 7**

6. **Application of Heronâ€™s Formula in Finding Areas of Quadrilaterals:** Let ABCD he a quadrilateral to find the area of a quadrilateral we need to divide the quadrilateral in triangular parts.

Area of quadrilateral ABCD = Area of Î”ABC + Area of Î”ADC

**Herons Formula Class 9 Notes Pdf Chapter 7**

### NCERT Notes for Class 9 Maths

- Chapter 1 Number Systems Class 9 Notes
- Chapter 2 Polynomials Class 9 Notes
- Chapter 3 Introduction to Euclid’s Geometry Class 9 Notes
- Chapter 4 Lines and Angles Class 9 Notes
- Chapter 5 Triangles Class 9 Notes
- Chapter 6Â Coordinate Geometry Class 9 Notes
- Chapter 7 Heron’s Formula Class 9 Notes
- Chapter 8Â Linear Equations in Two Variables Class 9 Notes
- Chapter 9 Quadrilaterals Class 9 Notes
- Chapter 10 Areas of Parallelograms and Triangles Class 9 Notes
- Chapter 11 Circles Class 9 Notes
- Chapter 12 Constructions Class 9 Notes
- Chapter 13 Surface Areas and Volumes Class 9 Notes
- Chapter 14 Statistics Class 9 Notes
- Chapter 15 Probability Class 9 Notes

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