Introduction
Previously we have studied about perimeter and area of different plane geometrical figures. We know that the magnitude of region bounded by plane figures is area. In this chapter we will learn more about area of plane and solid figures (like triangle quadrilateral, cube, cuboid, etc.)
Parallel Lines
Two lines are said to be parallel if the distance among them always remains same at each and every point. The parallel lines never intersect each other.
In other words we can say that if two lines do not have any common point than they are said to be parallel. In the figure I and m are parallel lines.
Concept of Transversal
Transversal is a line which intersects two or more parallel lines. In the figure, n is a transversal line.
Alternate Interior Angles
In the above figure
\[\angle 3\]and \[\angle 5,\text{ }\angle 4\]and \[\angle 6\]are alternate interior angles.
Alternate Exterior Angles more...
Angle
If two rays have common end point then the inclination between two rays is called angle. In the figure O is the vertex, \[\overline{OP}\] and \[\overline{OQ}\] are called arm of the angle. It is represented by notation\[\angle \].
Types of angle
Acute Angle
Tangle whose measure is more than \[0{}^\circ \] and less than \[90{}^\circ .\]
Right Angle
The angle of measure \[90{}^\circ \]
Obtuse Angle
The angle whose measure is more than 90° and less than \[180{}^\circ .\]
Straight Angle
The angle whose measure is \[180{}^\circ \]
Reflex Angle
The angle whose measure is more than \[180{}^\circ \]and less than \[360{}^\circ .\]
Complete more...
Some Terms Related to Lines
Point
It is a dimensionless figure which represents exact position. It is represented by a fine dot. We denote point by capital letters like A, B, C..........
Line Segment
It is the straight path between two points. In other words we can say that it has two end points and is of finite length.
Ray
When line segment extends infinitely in one direction is a ray. Simply we can say that a ray has one end point and definite length.
Line
When both end of more...
Introduction
In our daily life we observe different geometrical shapes. These geometrical shapes are not only the matter of study of mathematics but are directly related with our daily, life basic geometrical figures which make these geometrical shapes are lines and angles.
Introduction
Percentage is a fraction whose denominator is 100. The numerator of the such fraction is called the rate percent. For example 15 percent means \[\frac{15}{100}\] and denoted by 15 %.
Percentage
a % means \[\frac{a}{100}\] and simplify it. e.g. \[45%=\frac{45}{100}=\frac{9}{20}\]
For conversion of fraction \[\frac{p}{q}\] as percentage, we simply multiply it by 100 and put the sign of % or mathematically we can write \[\frac{p}{q}=\left( \frac{p}{q}\times 100 \right)%\]
The population of a village is \[4500.{{\left( \frac{11}{18} \right)}^{th}}\] of them are males and the rest are females. If 40 % of the females are married, then the number of married females is:
(a) 1750
(b) 700
(c) 750
(d) 900
(e) None more...
Application Based Problem on Percentage
The following are the points to remember to solve the problem related to variation in the price of an article.
In the new budget, the price of petrol increased by 25 %. By how much % person should reduce his consumption so that his expenditure is not affected
(a) 10%
(b) 20%
(c) 25%
(d) 30%
(e) None of these
Answer: (b)
Explanation more...
Introduction
In our day to day life we exchange the things with the money with others. During such transaction either we get profit or loss. In this chapter we will frequently use the term profit, loss, profit percent and loss percent.
Terms Related to Profit and Loss
Cost Price
It is the price of an article at which the shopkeeper purchases the goods from manufacturer or wholesaler. In short it can be written as C.P.
Selling Price
It is price of the article at which it is sold by the shopkeeper to the customer. In short it can be written as S.P.
Profit and Profit Percent
If the S.P. of an more...
Discount
In our daily life whenever we go to the market, we see banners & big hoardings indicating discount or sale up to 50 % off or buy one get one free. These are different tacts to attract the customers to the market. Shopkeepers want to get maximum rice for their goods and the customers are willing to pay as less as possible. Shopkeepers also offer different types of rebates in order to increase the sales or to finish old or damaged stock. This types of rebate on the price of article is called discount.
Marked Price
The price of an article which is indicated on it is called marked price or list price. In short form, it can be written as M.P. The amount which is to be reduced from marked price is called more...
Introduction
In our daily life the transaction of money is a common phenomenon in business where transaction involves large amount of money. Money is borrowed from bank Sum from individuals for certain duration of time and at certain rate of interest. The sum further returned to the specified person or bank including the interest on the original sum. Interest is that excess money paid on borrowed amount.
The Interests are of two types:
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