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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

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