# Herons Formula class 9 Notes Mathematics

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## CBSE Guide Herons Formula class 9 Notes

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## 10 Mathematics notes Chapter 12 Herons Formula

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CBSE Class 09 Mathematics
Revison Notes
CHAPTER 12
HERON’S FORMULA

1. Area of a Triangle – by Heron’s Formula

2. Application of Heron’s Formula in finding Areas of Quadrilaterals

• Triangle with base ‘b’ and altitude ‘h’ is

${\text{Area }} = \frac{1}{2} \times (b \times h)$

• Area of an isosceles triangle whose equal side is $a$ = ${{{a^2}} \over 2}$ square units
• Triangle with sides a, b and c

(i) Semi perimeter of triangle s =$\frac{{a + b + c}}{2}$

(ii) Area=$\sqrt {s(s - a)(s - b)(s - c)}$sq. unit

• Equilateral triangle with side ‘a’

Perimeter = $3a$ units

Altitude = ${{\sqrt 3 } \over 2}a$ units

${\text{Area }} = \frac{{\sqrt 3 }}{4}{{\text{a}}^2}{\text{ square units}}$

• Rectangle with length $l$, breadth $b$

Perimeter = $2\left( {l + b} \right)$

Area = $l \times b$

• Square with side $a$

Perimeter = $4a$ units

Area = ${a^2}$  sq. units

Area = ${\left( {{\rm{Diagonal}}} \right)^2}$ sq. units

• Parallelogra with length $l$, breadth $b$ and height $h$

Perimeter = $2\left( {l + b} \right)$

Area = $b \times h$

• Trapezium with parallel sides ‘a’ & ‘b’ and the distance between two parallel sides as ‘h’.

${\text{Area }} = \;\frac{1}{2}(a + b)h\;\;{\text{square units}}$