What is a prism ?.

What is Prism

• A prism is a 3-dimensional shape with two identical shapes facing each other. These identical shapes are called “bases”. 

• The bases can be a triangle, square, rectangle or any other polygon. 

• Other faces of a prism are parallelograms or rectangles.

Cross Section of Prisms

The cross section of a geometric shape or an object is the shape obtained by cutting it straight. It is also referred to as the intersection of a plane with the three-dimensional object. The cross section of a prism parallel to the base of the prism is same as its base.

• Triangular Prism

• Cube

Regular and Irregular Prism

The base of a prism can be a regular or irregular polygon. Based on the shape of the base, prisms are regular or irregular prisms.

• Regular Prism

• Irregular Prism

Surface Area and Volume of a Prism

The surface area of a prism is the sum of the area of all its faces. 

Volume of a prism is the amount of space inside the prism. 

Let us see how to find the surface area and volume of a triangular prism.

• Surface Area

Surface Area = Area of base triangles + Area of side parallelograms

= 2 × (12 x b x h) + 2 × (l x s) + (l x b) 

= bh + 2ls + lb

• Volume

Volume = Area of base triangle × length

= (12 b x h) × l

=12 bhl

Example: Calculate the surface area and volume of the following prism.

Length (l) = 12 cm, Height (h) = 4 cm, Base (b) = 6 cm, Side (s) = 5 cm

Surface area = bh+2ls+lb = 6 × 4 + 2 × 12 × 5 + 12 × 6  = 24 + 120 + 72  = 216 cm2

Volume = 12 bhl =12 × 6 × 4 × 12 = 144 cm3

Right Prism and Oblique Prism

When the two bases of a prism are perfectly aligned and its faces are rectangles (perpendicular to the bases) it is a right prism, else it is an oblique. They are characterized as follows:

• Right Prism

• Oblique Prism

	Right Prism	Oblique Prism
Height	The height is a lateral edge.	Height is an altitude outside the prism.
Side faces	Side faces are rectangles.	Sides faces are parallelograms.
Surface Area	bh+2ls+lb	bh+2ls+lb
Volume	12 bhl	12 bhl

The prisms are polyhedrons or objects with multiple flat faces. A prism can not have any side which is curved thus objects like cylinder, cone or sphere are not prisms.

Braches of mathematics

 

    What are the Branches of Mathematics?

  Mathematics can be broadly grouped into the following branches:

• Arithmetic: It is the oldest and the most elementary among other branches of mathematics. It deals with numbers and the basic operations- addition, subtraction, multiplication, and division, between them.
• Algebra: It is a kind of arithmetic where we use unknown quantities along with numbers. These unknown quantities are represented by letters of the English alphabet such as X, Y, A, B, etc. or symbols. The use of letters helps us to generalize the formulas and rules and also helps you find the unknown missing values in the algebraic expressions and equations.
• Geometry: It is the most practical branch of mathematics that deals with shapes and sizes of figures and their properties. The basic elements of geometry are points, lines, angles, surfaces and solids.

There are some other branches of mathematics that you would deal with in the higher classes.

• Trigonometry: Derived from two Greek terms, i.e., trigon (means a triangle) and metron (means measurement), it is the study of relationships between angles and sides of triangles.
• Analysis: It is the branch that deals with the study of the rate of change in different quantities. Calculus forms the base of analysis.

   List of branches of Maths

  Pure Mathematics:

• Number Theory
• Algebra
• Geometry
• Arithmetic
• Combinatorics
• Topology
• Mathematical Analysis

  Applied Mathematics

• Calculus
• Statistics and Probability
• Set Theory
• Trigonometry

Mathematics

ETYMOLOGY

The term "Mathematics" is derived from two Greek words: 

             'Manthanein' means' learning' 

             'Techne' means 'an art (or) technique'.

 Hence Mathematics means the art of learning related to disciplines (or) facilities.

DEFINITIONS

C.F.  Gauss: "Mathematics is the queen of science and Arithmetic is the queen of all Mathematics." 

Bacon: "Mathematics is the gateway and key to all science." -

Benjamin Franklin: "What science can there be more noble, more excellent,  more useful for men, more admirable, high and demonstrative than that of Mathematics? "

Desecrates: Mathematics is the science of order and measure." 

Aristotle: "Mathematics is the study of quantity." 

Bertrand Russell: "Mathematics is a subject identical with logic".

NATURE OF MATHEMATICS

Mathematics is the gate way of all science. In school those subject which are included in the curriculum must have certain aims and objectives on the basis of which its nature is decided. Now we are in position to conclude the nature of mathematics. The nature of Mathematics are enlisted in the following points,

• ·    Mathematics is an exact science. Mathematical knowledge is always clear, logical and systematic   and that may be understood easily.
• ·     It is the science of space, numbers, magnitude and measurement.
• ·     Mathematics involves conversion of abstract concepts into concrete form.
• ·     It is the science of logical reasoning.
• ·     It helps the man to give exact interpretation to his ideas and conclusion.
• ·     Mathematics is that science which is by product of out empirical knowledge.
• ·     Mathematical propositions are based on postulates and axioms from our observations.
• ·     It may exhibit abstract phenomenon into concrete. Thus abstract concepts may be explained and    understood with the help of mathematics.
• ·     It is related with each aspect of human life.
• ·     Mathematical knowledge is developed by our sense organs therefore it is exact and reliable.
• ·    The knowledge of Mathematics remains same in the whole universe, everywhere and every time.  It is not changeable.
• ·    The knowledge of mathematics has no doubt. It provides clear and exact response like yes or no, right or wrong.
• ·     It involves inductive and deductive reasoning and can generalize any proposition universally.

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