Introduction
Comprehension means 'Understanding'. Answering question to a given passage depends actually on the following abilities of a student:
(i) How good you are in understanding the meaning of the entire passage.
(ii) How good you are in finding the answers in the passage.
Points to keep in mind while doing Comprehension
Bar Graph
When the data is represented on the graph using bars the graph is known as Bar graph. In the following table, number of employee in different companies has been shown.
| Company | Number of employee |
| Company A | 300 |
| Company B | 700 |
| Company C | 500 |
| Company D | 400 |
| Company E | 500 |
| Company F | 800 |
| Company G | 400 |
Pictograph
When the data is represented on the graph with the help of pictures the graph is known as Pictograph. Let's understand how to make the pictograph. Number of cycles sold by a shop in a week has been shown in the following table:
| Day | Number of Cycles |
| Monday | 20 |
| Tuesday | 25 |
| Wednesday | 15 |
| Thursday | 20 |
| Friday | 30 |
| Saturday | 25 |
Step 2: Now choose a convenient scale in order to easily preparing the pictograph. Like one
represents 5 cycles
Thus, the number of cycles sold by the shop on Monday
Number of cycles sold by the shop on Tuesday
Number of cycles sold by the shop on more... 
Data
The information which is collected in the form of numerals called data. The population of Hong - Kong is 7008300, here 7008300 is a numeral which contains information about the population of Hong-Kong. So it is a data.
Raw Data
The initial data that the observer collects himself is called raw data. Like Jennifer asks to her class mates about their age one by one and note them which is as 8, 7, 6, 5, 7, 9, 8, 8, 8, 7, 9, 8, 10. It is the initial data which has been collected by the observer (Jennifer) herself. So it is a raw data.
Grouped Data
To extract the information contained by the data easily, the data is arranged in ascending or descending order using tables. In the above, it is not easy to extract certain information from the data collected by Jennifer because it is not arranged in any specific order. Let's arrange the data collected by Jennifer in ascending order 5, 6, 7, 7, 8, 8, 8, 8,9, 9, 10. This form of data is called grouped data. 
Introduction
In our day to day life, time to time we come across graphs like while reading books, watching news, etc. The graphs are prepared with the help of data. Data is collected through survey or other means. Then data is arranged in ascending or descending order using table. In this chapter, we will study about graphs, how to make the graphs and how to extract information contained by the graphs. 
Perimeter
As you know all the geometrical shapes like triangles, quadrilaterals, etc. occupy some area. Perimetre is referred as the length of the boundary line which subtend the area. In the rectilinear figure the area is bounded by the line segments are called sides. Thus perimetre can be referred as the sum of the length of the total sides.
Dotted line in the above figures shows perimetre.
Perimetre of the Triangles
Triangle is a one of the most simple shape of geometry which is made up of three sides. So to find the perimetre of the triangle we add length of all the three sides of the triangle.
Thus, perimetre of a triangle = Sum of length of all three sides.
Perimetre of the triangle \[\text{ABC}=\text{AB}+\text{BC}+\text{CA}\]
Find the perimetre of the given triangle.
Solution:
Perimetre of the triangle \[\text{PQR=PQ}+\text{QR}+\text{RP}\] \[=\text{6}.\text{5 cm}+\text{4 cm}+\text{7 cm}=\text{17}.\text{5 cm}\]
Perimetre of an Equilateral Triangle
All three sides of an equilateral triangle are equal so to find the perimetre of a triangle we multiply the length of one side of the triangle by 3. Thus, perimetre of an equilateral triangle \[=\text{3}\times \text{side}\]
Perimetre of the triangle \[\text{ABC}=\text{3}\times \text{AB}\]
Find the perimetre of the triangle PQR.
Solution:
Perimetre of an equilateral triangle \[=\text{3}\times \text{side}\]
In the triangle PQR Perimetre of the triangle \[~\text{PQR}=\text{3}\times \text{PQ}\] \[=\text{3}\times \text{3}.\text{5 cm}=\text{1}0.\text{5 cm}\]
Perimeter of an Isosceles
Triangle An isosceles triangle has two equal sides. So to find the perimetre of an isosceles triangle, we multiply length of one of the equal sides by 2 then add the length of third side. Thus perimetre of an isosceles triangle \[=\text{2}\times \] length ofone of the equal sides + length of the third (unequal) side
Perimetre of the triangle \[\text{ABC}=\text{2}\times \text{AB}+\text{BC}\]
Find the perimetre of the triangle PQR.
Solution:
Perimetre of an isosceles triangle\[=2\times \text{length}\] of one of the equal sides + length of unequal side In the triangle PQR Perimeter of the triangle \[\text{PQR}=\text{2}\times \text{PQ}+\text{QR}=\text{2}\times \text{5 cm}+\text{4 cm}=\]\[\text{14 cm}\]
Perimeter of an Scalene
Triangle In an scalene triangle all three sides are of different length. So to find the perimeter of an scalene triangle we add the length of all the more... 
Area
Look at the following pictures:
Shaded part in the figures given above represents area. So area is a mathematical term which tell us how much surface a particular object requires to be placed. Thus, we can say that area is the amount of surface which a particular object occupies.
Let us study about the area of some geometrical figures.
Area of a Triangle
Area of a triangle is half of the product of the base and corresponding height. So to find the area of a triangle we multiply the base and corresponding height of the triangle and then divide the product by 2.
Thus Area of a triangle\[=\frac{1}{2}\times \text{Base}\times \text{Height}\]
Area of the triangle \[\text{ABC}=\frac{1}{2}\times \text{AD}\times \text{BC}\]
Height
In a triangle, the length of the line segment which joins one vertex to the opposite side (on extending or without extending) making the angle of 90° is called height of the triangle.
LO, PQ and AD are heights of the triangles \[\Delta \text{LMN},\Delta \text{PQR}\] and\[\Delta \text{ABC}\]respectively.
Base
Base is the side of the triangle to which height is drawn.
BC, LN and PQ are the bases of the triangles \[\Delta \text{ABC},\text{ }\Delta \text{LMN},\]and\[\Delta \text{PQR}\]respectively.
Find the area of the triangle ABC as shown in the following figure.
Solution:
Area of the triangle\[\text{ABC}=\frac{1}{2}\times \text{Base}\times \text{Height}\] \[=\frac{1}{2}\times \text{BC}\times \text{AD}=\frac{1}{2}\times \text{7cm}\times \text{1}0\text{ cm}=\text{35 c}{{\text{m}}^{\text{2}}}\].
Area of a Rectangle
Area of a rectangle is equal to the product of its length and breadth. So to find the area of the rectangle we multiply the length of the rectangle by breadth of the rectangle. Thus area of a rectangle\[=\text{Length}\times \text{Breadth}\]
Area of the rectangle\[~\text{ABCD}=\text{AB}\times \text{BC}\]
Length
The longer side of a rectangle is called length of the rectangle.
Look at the following figure:
AB or CD is the length of the rectangle ABCD
Breadth
The smaller side of a rectangle is called breadth of the rectangle.
Look at the following figure:
PR or QS is the breadth of the rectangle PQRS.
Find the area of the given rectangle.
Introduction
In the previous chapter we have studied about the shape and size of some geometrical figures. In this chapter we will study about area and perimeter of some close geometrical figures. Area is referred as the amount of surface occupied by the geometrical shape whereas Perimetre is referred as the length of the boundary line which subtend the area occupied by the geometrical shape. Let us study about them in detail. 
Introduction In our day to day life we come across a number of objects. All the objects has a specific shape and size. See the following figures: (a) 
(b) 
(c) 
(d) 
(e) 
We recognize a number of objects by their shapes. Therefore, to know about the objects, being aware about their shape is very important. In this chapter we will study about the shapes of different geometrical figures. 
Point To show a particular location, a dot (.) is placed over it, this dot is known as point. 
In the above figure, point A shows the location of India, point B shows the location of Australia, point C shows the location of Russia, point D shows the location of China, point E shows the location of Iran, point F shows the location of Algeria. 
Look at the following figure, and name the point which shows the location of Bangalore on the map? 
Solution: Point (e) shows the location of Bangalore on the map. Arrow and End Point Before understanding line, line segment, and ray, let us understand meaning of Arrow and End point. Ø Arrow: Arrow at end of a line segment indicates that the line can be extended up to infinity in that direction. Ø End point: End point of a line segment indicates that where does the line segment come to end. Line Segment Line segment is defined as the shortest distance between two fixed points. 
It is denoted as\[\overline{\text{AB}}\]. Features of a Line Segment Ø A line segment has two end points. Ø A line segment has fixed length. 
Ø Line segment PQ, has two end points P and Q. Ø Line segment PQ has fixed length of 5 cm. Name all the line segments given in the figure. 
Solution: \[\overline{\text{AB}},\text{ }\overline{\text{BC}},\text{ }\overline{\text{CD}},\text{ }\overline{\text{DA}},\text{ }\overline{\text{AC}},\text{ }\overline{\text{BD}},\text{ }\overline{\text{OA}},\text{ }\overline{\text{OB}},\text{ }\overline{\text{OC}},\text{ }\overline{\text{OD}}\] Ray It is defined as the extension of a line segment in one direction up to infinity. 
It is denoted as ha Features of a Ray (a) A ray has only one end point. (b) A ray has an arrow at its one end, which shows that the ray can be extended up to infinity in one direction. (c) Length of a ray cannot be measured. 
(a) P is the end point of the ray PQ. more... 
Circle
Circle is a close curved line whose all points are at the same distance from a given point in a plane.
Centre of a Circle
The point from which all the points of the curved line are at the same distance is called centre of the circle.
In the given figure, 0 is the centre of the circle.
Radius of a Circle
Distance between the centre and the curved line of a circle is called radius of the circle.
In the given figure, OA is the radius of the circle. Note: All the radius of a circle are equal in length.
Chord of a Circle
Any line segment which joins the two points of the curved line of a circle is called chord of the circle.
In the figure, AB is the chord of the circle.
Diameter of a Circle
The longest chord of a circle is called diametre of the circle. In other word the chord which passes through the centre is called diametre of the circle.
In the figure, AB is the diametre of the circle
Note: All the diametres of a circle are equal in length.
Relation between Radius and Diametre of the Circle
In a circle, diametre is twice of the radius. Let radius of a circle is r then diameter of the circle is 2r.
In the given circle, OM and ON are the two radius of the circle whereas MN is the diametre of the circle. We can see, MN = OM + ON ..........(i)
We know that all the radius of a circle is equal in length. Thus OM = ON ..........(ii)
So, we can write the equation (i) as followings: ' \[\text{MN}=\text{OM}+\text{OM or MN}=\text{ON}+\text{ON}\] Thus MN = 20M or MN = 2ON Thus, we see that the diametre of a circle is twice of the radius.
Radius of a circle is 5 cm. Find the diametre of the circle.
Solution: \[\text{Diametre}=\text{2}\times \text{radius}\] \[=\text{2}\times \text{5cm}\] =10 cm.
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