 # Class 9 Maths notes for Heron Formula | Mensuration

Notes Assignments Ncert Solutions Revision sheet

## Mensuration

• It is branch of mathematics which is concerned about the measurement of length ,area and Volume of plane and Solid figure

## Perimeter

• The perimeter of plane figure is defined as the length of the boundary
• It units is same as that of length i.e. m ,cm,km
 1 Meter 10 Decimetre 100 centimetre 1 Decimetre 10 centimetre 100 millimetre 1 Km 10 Hectometre 100 Decameter 1 Decameter 10 meter 1000 centimetre

## Area

• The area of the plane figure is the surface enclosed by its boundary
• It unit is square of length unit. i.e. m2 , km2
 1 square Meter 100 square Decimetre 10000 square centimetre 1 square Decimetre 100 square centimetre 10000 square millimetre 1 Hectare 100 squareDecameter 10000 square meter 1 square myraimeter 100 square kilometre 108 square meter

## Perimeter and Area of Different Figure

 N Shape Perimeter/height Area 1 Right angle triangle Base =b, Height =h Hypotenuse=d $P=b+h+d$ Height =h $A=\frac {1}{2}BH$ 2 Isosceles right angled triangle Equal side =a Height=a $A=\frac {1}{2} \sqrt {a}$ 3 Any triangle of sides a,b ,c $P=a+b+c$ $A=\sqrt {s(s-a)(s-b)(s-c)}$ $s=\frac {a+b+c}{2}$ This is called Heron's formula (sometimes called Hero's formula) is named after Hero of Alexandria 4 Square Side =a $A=a^2$ 5 Rectangle of Length and breath L and B respectively $P=2L +2B$ $A=L \times B$ 6 Parallelograms Two sides are given as a and b $P=2a+2b$ $A= Base \times height$ When the diagonal is also given ,say d Then $A= \sqrt {s(s-a)(s-b)(s-d)}$ $s=\frac {a+b+d}{2}$ 7 Rhombus Diagonal d1 and d2 are given $p=2 \sqrt {d_1^2+d_2^2}$ Each side=$\frac {1}{2} \sqrt {d_1^2+d_2^2}$ $A=\frac {1}{2} d_1 d_2$ 8 Quadrilateral a. All the sides are given a,b,c ,d b. Both the diagonal are perpendicular to each other c. When a diagonal and perpendicular to diagonal are given a. $P=a+b+c+d$ a. $A=\sqrt {s(s-a)(s-b)(s-c)(s-d)}$ $s=\frac {(a+b+c+d)}{2}$ b. $A=\frac {1}{2} d_1 d_2$ where d1 and d2 are the diagonal c. $A=\frac {1}{2} d(h_1+h_2)$ where d is diagonal and h1 and h2 are perpendicular to that

## How to solve the Area and Perimeter problems

1. We must remember the formula for all the common figures as given above the table
2. Find out what all is given in the problem
3. Convert all the given quantities in the same unit
4. Sometimes Perimeter is given and some side is unknown,So you can calculate the sides using the Perimeter
5. If it is a complex figure ,break down into common know figures like square,rectangle,triangle
6. Sometimes we can find another side using Pythagoras theorem in the complex figure
7. If common figure, apply the formula given above and calculate the area.
8. If complex figure, calculate the area for each common figure in it and sum all the area at the end to calculate the total area of the figure

## Solved Examples

1. A right angle triangle has base 20 cm and height as 10 cm, What is the area of the triangle?
Solution
Given values B=20 cm
H=10 cm
Both are in same units
A=(1/2)BH=100 cm2
2. Sides of triangles are in the ratio 12:17:25. The perimeter of the triangle is 540 cm. Find out the area of the triangle?
Solution
Let the common ration between the sides be y,then sides are 12y,17y,25 y
Now we know the perimeter of the triangle is given by
P=a+b+c
540=12y+17y+25y
or y=10 cm
Now Area of triangle is =[s(s-a)(s-b)(s-c)]1/2
Where s=(a+b+c)/2
Here s=270 cm
a=120 cm
b=170cm
c=250cm
Substituting all these values in the area equation,we get
A=9000cm2
3. A equilateral triangle is having side 2 cm. What is the area of the triangle?
Solution:
We know that Are of equilateral triangle is given by
A=[(3)1/2 a2]/4
Substituting the values given above
A=(3)1/2

## We can summarize various method to calculate the Area of the Triangle

 If you know the altitude and Base Area =(1/2)BH If you all the three sides A=[s(s-a)(s-b)(s-c)]1/2 s=(a+b+c)/2 If it is isosceles triangle with equal side a A=(1/2)a1/2 If it is equilateral triangle with equal side a A=[(3)1/2 a2]/4 If it is right angle triangle with Base B and Height H Area =(1/2)BH

Reference Books for class 9 Math

Given below are the links of some of the reference books for class 9 Math.

1. Mathematics for Class 9 by R D Sharma One of the best book for studying class 9 level mathematics. It has lot of problems to be solved.
2. Secondary School Mathematics for Class 9 by R S Aggarwal This is also as good as R.D. Sharma. Either this or the book by R.D. Sharma will do. I find book R.S. Aggarwal little bit more challenging than the one by R.D. Sharma.
3. Pearson IIT Foundation Series - Maths - Class 9 Buy this book if you want to challenge yourself further and want to prepare for JEE foundation.
4. Pearson IIT Foundation Physics, Chemistry & Maths combo for Class 9 Only buy if you are prepared to study extra topics and want to take your studies a step further. You might need help to understand topics in these books.

You can use above books for extra knowledge and practicing different questions.

Note to our visitors :-

Thanks for visiting our website.