6 sided shape

6 sided shape:One of the most common examples of a 6 sided shape is our very own "DICE".A die (plural dice, from Old French dé, from Latin datum "something given is a small polyhedral object, usually cubic, used for generating random numbers or other symbols. This makes dice suitable as gambling devices, especially for craps or sic bo, or for use in non-gambling tabletop games.A traditional die is a cube (often with corners slightly rounded), marked on each of its six faces with a different number of circular patches or pits called pips. us next learn about the 7 sided polygon,In geometry a polygon (pronounced /ˈpɒlɪɡɒn/) is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments (i.e., by a closed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.Hope you like the above example of 6 sided shape.Please leave your comments, if you have any doubts.

Area of the Quadrilateral

Area of the Quadrilateral: In quadrilateral the opposite sides are equal lengths; the opposite angles are equal; or that the diagonals bisect each other.In ABCD quadrilateral diagonal is a straight line joining two alter AC and DB are the diagonals.Areas of quadrilateral is measured in terms of square units such as square inches,squarefeet or square meters.Now let us look at area of a quadrilateral problems.area of a quadrilateral problems, Areas of quadrilaterals = √{(s-a)(s-b)(s-c)(s-d) -1/4(ac+bd+pq)(ac+bd-pq)}, where a,b,c and d are the four sides of the quadrilateral, p and q are diagonals, and s = (a+b+c+d)/2.Let us now calculate the area of a quadrilateral.


You can achieve the same result with this formula:

Areas of a quadrilateral Problem = √{(s-a)(s-b)(s-c)(s-d)-abcd(cos square theta)}

where theta = 1/2 (sum of two opposite angles)

Another method:

The area of quadrilateral ABCD = 1/2Area of ABD +1/2 area of BDC

= ½ x base x altitude + ½ x base x altitude

= 1/2d ( h1 + h2)

Hope you like the above example of Area of the Quadrilateral.Please leave your comments, if you have any doubts.

Least Common Multiple

Least Common Multiple:In arithmetic number of theory is the least common multiple or lowest common multiple (LCM) or smallest common multiple of two integers a and b is the smallest positive integer that is a multiple of both of a and of b. Since it was a multiple, it can be divided by a and b without a reminder. If either a or b is 0, so that number is no such positive integer, then LCM(a, b) is defined to be zero.Let us understand the L.C.M with an example.Example 1:Find lowest common multiple for the number 24 and 34.

On finding the LCM we have to find the prime factors for the given number.

24 : 2 2 2 3

34 : 2 17

---------------------------

LCM : 2 2 2 3 17

Lowest common multiple for the numbers 24 and 34 is 2 * 2 * 2 * 3 * 17 = 408.In this blog a simple explanation is given about math least common multiple-L.C.M.Hope you like the above example of Lower Common Multiple.Please leave your comments, if you have any doubts.

Distance formula

Distance formula:Find the distance between the following pair of points:

A (1,2) and B (4,5).
Suggested answer:

Using the distance formula,

The next important thing that we will learn is Distance Formula Math:
* The distance method can be obtained by generate a triangle and with the Pythagorean Theorem to locate the length of the hypotenuse.
* The hypotenuse of the triangle will be the distance connecting the double points.
* The subscripts refer to the original and next points; it doesn't material which points you call original or next.

Let us now see Formula of Distance :

Distance = [sqrt((y2-y1)^2 + (x2 -x1)^2))]

Here (x1, y1) and (x2, y2) are the end points of the line segment. We need to find the distance the two points.Hope you like the above example of Complex Numbers.Please leave your comments, if you have any doubts.

Sets and relations

Sets and relations:

Introduction about sets and relations:

A group of elements is called a set when the elements in the group are distinct. A characteristic of two objects is called Relation
.
Example of a Set:

• The collection of all natural numbers
• The collection of all equilateral triangles in a plane.

Let us learn more about sets and relations in this chapter.

A relation is a set of ordered pairs(x,y) , where the first component of the ordered pairs are the input values and the second component are the output values.

Set of all Input Values is known as Domain of the given Relation.

Similarly, set of all Output Values is known as Range of the given Relation.

Mathematically,

A relation R defined by ( , {(x,y):x }) ,is the set of ordered pairs of all Input Values (x) and all Output Values(y) such that each element x is related to the corresponding element y.

Here,

x=Domain of the Relation and

y=Range of the Relation

iff no values of x and y is repeated.

x is called Independent variable and y is called Dependent variable because its value depends on the x-value chosen.The most commonly asked question is how do we express a relation,we come across this question very frequently. Relation scan be represented in any of the following forms:-

(i) Roster form

This method is also known as Tabular method. In this method, a set is represented by writing all the elements of the set, separated by commas and are enclosed withinbrackets { }.

For e.g. D = {Sunday, Monday, Tuesday,, Wednesday, Thursday, Saturday}.

Lets take some examples to show the relation in various forms:-

(ii) Set builder form Set builder notation has the form {x : f(x)} (some write {x | f(x)}, using the vertical bar instead of the colon), denoting the set of all individuals in the universe of discourse satisfying the formula f(x), that is, the set whose members are every individual x such that f(x) is true.For e.g. is the set of all positive real numbers.

(iii) By tables

Table representation of the RelationInputOutputa3c2e9
(iv) Arrow diagram :-

(v) By graphs:-

Hope you like the above example of Sets and Relations. .Please leave your comments, if you have any doubts.

Laws of Exponent

Laws of Exponent:

Introduction to Exponents:

Exponent is a math function symbolize by 2 parts ,

is the base.
is the exponent.

The exponent says the number of times the base must be multiplied by it self, Exponent is the part of algebra and they have defined properties, with the help of it we can simplify the given exponent expressions.

Now lets see the laws of exponents.

The laws of exponents are used for combining exponents of numbers. Exponents is a number raised to another number, it is denoted as, a ⁿ, here, n is known as the exponent of the nth power of a.

Pythagoras Theorem

Pythagoras Theorem:

The Pythagoras Theorem is the theorem which is developed by a Greek mathematician named Pythagoras, for finding the sides of any right angle triangle. It is also used to verify the triangle is Right angle triangle or not. According to him, the sum of square of two smaller sides is equal to the square of largest side. It is given by the formulae,

According to Pythagorean Theorem: c² = a² + b².

The longest side of a right angle triangle is always directly across from the 90 degree angle is the hypotenuse. The other two sides are called as legs.

Students may have heard of the Pythagoras Theorem and the problems related to the theorem, but are uncertain about how to solve these kinds of problems or why they would be important in their everyday lives.

To start with, the student should understand that two lines intersect in a point, called a "vertex" and the circular span between the lines is called an angle.A 90 degree angle is the right angle.


Practice Problems on Pythagoras Theorem Learning

Learn to find the missing measure of leg of the right triangle if hypotenuse is 10 cm and right side is 6cm.

The figure is given above for reference.

Hope you like the above example of Pythagoras Theorem.
Please leave your comments, if you have any doubts.