Mensuration
Mensuration is the branch of mathematics which deals with the measurement of lengths, area and volume of the plane and solid figures.
Perimeter of a plane figure: The distance all round a plane figure is called perimeter of the figure or the lengths of boundary of a plane figure is known as its perimeter
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Perimeter of the quadrilateral \[ABCD=AB+BC+CD+DA\]
\[=40\text{ }cm+10\text{ }cm+40\text{ }cm+10\text{ }cm\]
\[=100\text{ }cm\]
Perimeter of the hexagon \[ABCDEF=AB+BC+CD+DE+EF+FA\]
\[=100\text{ }m+120\text{ }m+90\text{ }m+45\text{ }m+60\text{ }m+80\text{ }m\]
\[=495\text{ }m\]
Perimeter of a scalene triangle = Sum of all the three sides of the triangle.
Example: Find the perimeter of the triangle ABC.
Perimeter of the triangle \[ABC=AB+BC+CA\]
\[=4\text{ }cm+12\text{ }cm+8\text{ }cm\]
\[=24cm\]
Perimeter of a rectangle \[=2\times \left( length+breadth \right).\]
Example: Find the perimeter of the following rectangle ABCD.
Perimeter of rectangle \[ABCD=2\times \left( AB+BC \right)\]
\[=2\times \left( 15cm+9cm \right)\]
\[=48\text{ }cm\]
Perimeter of regular shapes
Perimeter of an equilateral triangle \[\text{=3 }\!\!\times\!\!\text{ length of one side}\].
Example: Find the perimeter of the given triangle.
Perimeter of the triangle \[=3\times 4\text{ }cm\]
\[=12\text{ }cm\]
Perimeter of a square: \[\text{4 }\!\!\times\!\!\text{ length of one side}\text{.}\]
Example: Find the perimeter of the given square.
Perimeter of the square \[=4\times 1\text{ }m\]
\[=4\text{ }m\]
Perimeter of regular pentagon \[=5\text{ }\times \text{ }length\text{ }of\text{ }one\text{ }side.\]
Example: Find the perimeter of the given pentagon.
Perimeter of the pentagon \[=5\times 4\text{ }cm\]
\[=20\text{ }cm\]
Perimeter of the regular hexagon \[=6\times length\text{ }of\text{ }one\text{ }side.\]
Perimeter of the hexagon \[=6\times 5\text{ }cm\]
\[=30\text{ }cm.\]
Area of a plane figure: The measurement of the region enclosed by a plane figure is called area of the figure or area is the amount of surface covered by the shape.
Area of triangle \[=\frac{1}{2}\times base\times height.\]
Example: Find the area of the given triangle.
Area of the triangle \[=\frac{1}{2}\times 4cm\times 6cm=12c{{m}^{2}}\]
Area of rectangle: \[length\times breadth.\]
Example: Find the area of the given rectangle.
Area of the rectangle \[=8\text{ }cm\times 6\text{ }cm=48\text{ }c{{m}^{2}}\] more...
Data
A collection of information in the form of numerical figures is called data.
Raw data: Data obtained in the original form is called raw data.
Tabulation of data: Arranging the data in a systematic form in the form of a table is known as tabulation of data.
Statistics
The branch of mathematics which deals with the collection, presentation, analysis and interpretation of numerical data is called statistics.
Example
A dice was thrown 30 times and the following outcomes were noted:
4, 3, 3, 2, 5, 4, 4, 6, 1, 2, 2, 3, 4, 6, 2, 3, 3, 4, 1, 2, 3, 3, 4, 5, 6, 3, 2, 1, 3, 4.
Represent the above data in the form of frequency distribution.
Explanation: We may present the data as shown below:
ALGEBRAALGEBRAThe part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.Introduction to Algebra
Variable: A letter symbol which can take various numerical values is called variable or literal.
Example: \[x,\,\,y,\,\,z\]etc.
Constant: A symbol which can take a fixed numerical value is called a constant.
Algebraic expression: A combination of constant and variable connected by mathematical operations \[(+,\,\,-,\,\,\times ,\,\,\div )\] is called an algebraic expression.
RATIO, PROPORTION AND UNITARY METHODRATIOThe comparison of two quantity of same kind by division is called ratio.Example: Ratio between Rs. 30 and Rs. 50, but there can be no ratio between Rs. 30 and 50 apples, form of ratio \[=x:y\]\[x\to \]antecedent\[y\to \]consequent
B The ratio of \[x\]to \[y\]
B \[x\]is to \[y\]
\[x:y\]
B \[x\]and \[y\] are called terms of ratio.
Types of Ratio:
Compound Ratio: Ratio is compound when antecedents are multiplied by respective antecedents and consequents are multiplied by respective consequents.
Example: \[a:b,\,\,c:d,\,\,e:f,\]then compound ratio is,\[\frac{a\times c\times e}{b\times d\times f}\]
Duplicate Ratio: If \[x:y\] is a ratio, then\[{{x}^{2}}:{{y}^{2}}\]is duplicate ratio.
GEOMETRYGEOMETRYGeometry is derived from two greek words "Geo" means "Earth" metron means "Measurement". That means measurement of Earth is called geometry.Basics terms of geometry
There are three basics undefined terms of geometry.
(i) Point (ii) Line (iii) PlanePoint: Point is a mark of position, it is made by sharp tip of pen, pencil and nail.
It is denoted by capital letter.
It is represented by
A point has no length, no breadth and no thickness.
Line segment: The distance between two points in a same plane is called a line segment.
It is denoted by\[\overline{AB}\]. It is measured in 'cm' or 'inch'.
MENTAL ABILITYFUNDAMENTALSMental Ability: The power to learn or retain knowledge, in law, the ability to understand the fact and significance of your behavior.
Mental ability develop logical thinking among students.
Mental ability is based on some concepts.
Series completion
Number series
Alphabet series
Number Series: The three or more numbers having a sequence of pattern is given. The numbers follow a certain rule which relates the consecutive terms. Students should be able to recognize the rule or pattern. This will be help them to find the next term or number.
Look at the example given below1.Series of odd number1, 3, 5, 7, 9, ___________Ans.: Next number is 11.2.Series of even number. more...
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Perimeter of the quadrilateral \[ABCD=AB+BC+CD+DA\]
\[=40\text{ }cm+10\text{ }cm+40\text{ }cm+10\text{ }cm\]
\[=100\text{ }cm\]
Perimeter of the hexagon \[ABCDEF=AB+BC+CD+DE+EF+FA\]
\[=100\text{ }m+120\text{ }m+90\text{ }m+45\text{ }m+60\text{ }m+80\text{ }m\]
\[=495\text{ }m\]
Perimeter of a scalene triangle = Sum of all the three sides of the triangle.
Example: Find the perimeter of the triangle ABC.
Perimeter of the triangle \[ABC=AB+BC+CA\]
\[=4\text{ }cm+12\text{ }cm+8\text{ }cm\]
\[=24cm\]
Perimeter of a rectangle \[=2\times \left( length+breadth \right).\]
Example: Find the perimeter of the following rectangle ABCD.
Perimeter of rectangle \[ABCD=2\times \left( AB+BC \right)\]
\[=2\times \left( 15cm+9cm \right)\]
\[=48\text{ }cm\]
Perimeter of regular shapes
Perimeter of an equilateral triangle \[\text{=3 }\!\!\times\!\!\text{ length of one side}\].
Example: Find the perimeter of the given triangle.
Perimeter of the triangle \[=3\times 4\text{ }cm\]
\[=12\text{ }cm\]
Perimeter of a square: \[\text{4 }\!\!\times\!\!\text{ length of one side}\text{.}\]
Example: Find the perimeter of the given square.
Perimeter of the square \[=4\times 1\text{ }m\]
\[=4\text{ }m\]
Perimeter of regular pentagon \[=5\text{ }\times \text{ }length\text{ }of\text{ }one\text{ }side.\]
Example: Find the perimeter of the given pentagon.
Perimeter of the pentagon \[=5\times 4\text{ }cm\]
\[=20\text{ }cm\]
Perimeter of the regular hexagon \[=6\times length\text{ }of\text{ }one\text{ }side.\]
Perimeter of the hexagon \[=6\times 5\text{ }cm\]
\[=30\text{ }cm.\]
Area of a plane figure: The measurement of the region enclosed by a plane figure is called area of the figure or area is the amount of surface covered by the shape.
Area of triangle \[=\frac{1}{2}\times base\times height.\]
Example: Find the area of the given triangle.
Area of the triangle \[=\frac{1}{2}\times 4cm\times 6cm=12c{{m}^{2}}\]
Area of rectangle: \[length\times breadth.\]
Example: Find the area of the given rectangle.
Area of the rectangle \[=8\text{ }cm\times 6\text{ }cm=48\text{ }c{{m}^{2}}\] more... 
\[\Rightarrow \] Let us see the chart of Indian system and understand about Indian system.
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