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Heron's Formula Class 9th Notes - Free NCERT Class 9 Maths Chapter 12 Notes - Download PDF

Heron's Formula Class 9th Notes - Free NCERT Class 9 Maths Chapter 12 Notes - Download PDF

Updated on Apr 23, 2025 11:11 AM IST

A triangle is a geometrical figure that has three sides and three corners, and three angles. It is a closed shape figure with the least number of sides. There are many types of triangles, and based on the properties, there are some formulas to calculate the area or perimeter of the triangle. The word triangle comes from the Latin word triangulus, and it means three-cornered or having three angles. Heron was a mathematician and engineer in Alexandria in Egypt, who derived the formula for calculating the area of triangles by using only the sides of the triangle. Triangles are used in many areas, like in construction, building design, sailing and navigation, art and design, pyramids, calculus, calculating distance, locating objects, etc.

This Story also Contains
  1. NCERT notes Class 9 Maths Chapter 12 Heron's Formula
  2. Area of a Triangle by Heron's Formula
  3. Class 9 Chapter Wise Notes
  4. NCERT Solutions for Class 9
  5. NCERT Exemplar Solutions for Class 9
  6. NCERT Books and Syllabus
Heron's Formula Class 9th Notes - Free NCERT Class 9 Maths Chapter 12 Notes - Download PDF
Heron's Formula Class 9th Notes - Free NCERT Class 9 Maths Chapter 12 Notes - Download PDF

These notes cover the basic definition of triangles, types of triangles, and formulae for calculating the area and perimeter of the triangle. CBSE Class 9 chapter includes examples for the given topics as required. Students must practice all the questions and examples to ace the topic. Subject Matter Experts designed the NCERT class 9th maths notes as per the latest syllabus. Students can download NCERT notes according to their standard and subjects.

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NCERT notes Class 9 Maths Chapter 12 Heron's Formula

Triangle: A geometrical closed figure that has three sides, three angles and three corners. The three corners are also called the vertices of the triangle.

Types of Triangles

Triangles can be divided into two categories:
1. Based on sides
2. Based on angels

Based on Sides

1. Equilateral Triangle
2. Isosceles Triangle
3. Scalene Triangle

Equilateral Triangle:

A triangle in which all sides are equal is called an equilateral triangle.

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Area of equilateral triangle = 34a2

Perimeter of equilateral triangle = 3a

Where,

a is the side of the triangle.

Example: Find the area and perimeter of the equilateral triangle, in which the length of the side is 10cm.

Area of equilateral triangle = 34102

= 253cm2

Perimeter of equilateral triangle = 3×10

= 30

Isosceles Triangle:

A triangle in which any two sides are equal is called an isosceles triangle.

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Area of isosclales triangle = 12bh

Perimeter of an isosceles triangle = 2a+b

Example: Find the area and perimeter of the triangle whose base is 12 cm long and each equal side is 16 cm long.

Area of isosclales triangle = 1212×16

Area of isosclales triangle = 96

Perimeter of an isosceles triangle = 2×16+12

Perimeter of an isosceles triangle = 44

Scalene Triangle

A triangle where the length of each side is different is known as a scalene triangle.

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Area of scalene triangle = 12bh

Perimeter of an scalene triangle = a+b+c

Area of a Triangle by Heron's Formula

Heron is a mathematician and an engineer in Alexandria in Egypt, he defined a formula to determine the area of a triangle when only all three sides are known. The Heron's formula for determining the area of a triangle is as follows:

Semiperimeter (S) = (a+b+c)2

Where a, b, and c are the sides of the triangle.

Area of triangle = s(sa)(sb)(sc)

Example: Find the area of a triangle whose sides are 4 cm, 5 cm and 7cm respectively.

Semiperimeter (S) = (a+b+c)2

Semiperimeter (S) = (4+5+7)2

Semiperimeter (S) = 8

Area of triangle = 8(84)(85)(87)

Area of triangle = 96cm2

Class 9 Chapter Wise Notes

Students must download the notes below for each chapter to ace the topics.

NCERT Solutions for Class 9

Students must check the NCERT solutions for Class 10 Maths and Science given below:

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NCERT Exemplar Solutions for Class 9

Students must check the NCERT exemplar solutions for Class 10 Maths and Science given below:

NCERT Books and Syllabus

To learn about the NCERT books and syllabus, read the following articles and get a direct link to download them.


Articles

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

Option 4)

K/4

In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

remain unchanged

Option 4)

be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1)

Molality

Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

half that in 8 g He

Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

Option 4)

more than 9

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