Topics
Number Systems
Real Numbers
Algebra
Pair of Linear Equations in Two Variables
- Linear Equation in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient
Arithmetic Progressions
Quadratic Equations
- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots of a Quadratic Equation
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Application of Quadratic Equation
Polynomials
Geometry
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem (Thales Theorem)
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity of Triangles
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity of Triangles
- Ratio of Sides of Triangle
Constructions
Trigonometry
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Statistics and Probability
Probability
Statistics
Coordinate Geometry
Lines (In Two-dimensions)
Mensuration
Areas Related to Circles
Surface Areas and Volumes
- Concept of Surface Area, Volume, and Capacity
- Surface Area of a Combination of Solids
- Volume of a Combination of Solids
- Conversion of Solid from One Shape to Another
- Frustum of a Cone
- Concept of Surface Area, Volume, and Capacity
- Surface Area and Volume of Different Combination of Solid Figures
- Surface Area and Volume of Three Dimensional Figures
Internal Assessment
Notes
So far, we have calculated the areas of different figures separately. Let us now try to calculate the areas of some combinations of plane figures.
Example 4 : In Fig., two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
For sector ODC,
∠DOC= θ= 90° (because O is the point of intersection of diagonals of square ABCD
`"Diagonal BD"= "side"sqrt2= 56sqrt2`
therefore, OD=r = `(56sqrt2)/2= 28sqrt2cm`
area of sector ODC= `θ/360 xx πr^2`
=`(90 xx 22 xx 28sqrt2 xx 28sqrt2)/360 xx 7`
`= 22 xx 2 xx 28`
area of sector ODC= `22 xx 56m^2`
area of ΔDOC= `1/2 xx OD xx OC`
= `1/2 xx 28sqrt2 xx 28sqrt 2`
area of ΔDOC= `19 xx 56m^2`
area of flower beds= `2 xx (22 xx 56)- (19 xx 56)`
=` 2 xx 56 (22-19)`
= `112 xx 8`
area of flower beds= `896m^2`
`"area" "of" "lawn"= "side"^2= 56^2`
`"area" "of" "lawn"= 3136m^2`
`"Total" "area" = 3136+896`
`"Total" "area" = 4032m^2`
