Triangle Area Equation

Introduction to triangle area equation:
In this article we discuss about the triangle area equation. The triangle can be defined as three closed sided polygon. To find the area of triangle is multiplying by the height and base, and then dividing by two. Basically the triangle comes from parallelogram. The parallelograms can be divided into two triangles. The each triangle area is equal to the one-half the area of the parallelogram. The parallelogram and triangle figure is given below,

Triangle Area Equation:

The area of parallelogram equation is given below,

`Area=Base xx Height`

That is, `A=B xx H`

The area of the triangle equation is given below,

Area of triangle=`"parallelogram"/2` or

Area= `(Base xx Height)/2` or

Area= `1/2 xx (B xx H)`

Where

B is the base of the triangle

H is the height of the triangle

We know the length of all sides of the triangle; we can calculate the area by using the Heron’s equation. Please express your views of this topic how to find the volume of a triangular prism by commenting on blog.

In this case first we have to define a perimeter of a triangle.

Perimeter= (a side + b side + c side)

Semi-Perimeter= `(a side + b side + c side)/2`

Therefore the heron’s equation is given below,

Area=`sqrt(s.(s-a).(s-b).(s-c))`

The all sides of the triangle figure is given below,

Example Problems for Triangle Area Equation:
Triangle area equation problem 1:

To find the area of a triangle with base 40 inches and height 6 inches?

Solution:

Given data: base (B) =40 inches and height (H) =6 inches.

Area of a triangle=`1/2` `xx` (B `xx` H)

=`1/2` `xx` (40 `xx` 6)

=`1/2 xx` 240

`Area = 120 i n^2`

Therefore the area of the triangle value is `120 i n^2` .

Triangle area equation problem 2:

A triangle has side a =10 in, side b =14 in and side c =12 in. Find its area?

Solution:

Given data: side a=10 in, side b=14 in, side c=12 in

First we find the perimeter of the triangle.

The perimeter = 10+ 14 + 12 = 36.

Next we find the semi-perimeter of the triangle.

The semi-perimeter is one half of this or 18

Using Heron's formula,

area = `sqrt (s . (s-10). (s-14) .(s-12))`

= `sqrt (18 . (18-10) .(18-14) . (18-12))`

= `sqrt (18 .(8) . (4) . (6))`

= `sqrt (3456)`

=  `58.78 i n^2`

Event Space Probability

Introduction to event space probability:

The event space determines the output in the probability that refers the total number of possibilities for the experiment. The sample spaces of the each experiment are not same. For example, the sample space for tossing the coin and the sample space for rolling the die and the sample space for the getting the diamond card from the group of cards are different. The sample spaces of the each experiment determine the probability for that event.I like to share this Simple Events with you all through my article.

Terms Used in the Event Space Probability:

Trial is the process of performing any experiment is called as the trial.
Sample space represents a set of all necessary outcomes of the experiment.
Event is a subset of a sample space whose elements are the outcomes of a trial.
Equally likely events are the events that none of the events can be performed as like as the other event.
Mutually exclusive events are the events that two events cannot occur simultaneously.
Exhaustive event contains the set of all possible outcomes for the experiment.
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Example Problems for Event Space Probability:

Example 1 for event space probability:

A bag contains the 12 red balls, 3 green balls and 7 black balls. What is the sample space for getting the balls?

Solution:

The bag contains the 12 red balls, 3 green balls and 7 black balls. The total numbers of balls are 22 balls.

The sample space is 22.

Example 2 for event space probability:

Determine the sample space for rolling the single die.

Solution:

The die contains six faces.

The sample space for the die is 6.

It can be represented in the form of S= {1, 2, 3, 4, 5, 6}.

Example 3 for event space probability:

Find the sample space for tossing two coins.

Solution:

A single coin has two sides. For the single coin the sample space is 2.

For two coins the sample space is 4.

Construct a Perpendicular

Introduction to Construct a Perpendicular

Constructing a perpendicular means drawing a line at right angles to a given line from a given point. In case of curves, the perpendicular from a given point is to the tangent of the curve at the required point. Constructing perpendicular can be done in two ways. One method is by using a ruler and protractor and the other method is with the help of a compass and a ruler.

The second method is more accurate and let us study that.

Construct a Perpendicular – when the Point is on the Line

Look at the above diagram. To construct a perpendicular line l at point A in the line itself, the method is as follows.

1)    Select two convenient points B and C on the line and on either side of A.

2)    Set the compass for a radius of approximately more than half of the length BC.

3)    Strike an arc from the point B..

4)    Without changing the compass setting strike an arc from the point C..

5)    Mark the point P where the arcs intersect.

6)    Draw a line m passing through P and A.

Line m is the perpendicular to the line l.

Construct a Perpendicular – from a Point not on the Line

In this diagram, the point A is not on the line. To construct a perpendicular in this case, the steps are as follows.

1)    With the help of the compass draw arcs from A to intersect the line at B and C.

2)    Set the compass for a radius of approximately more than half of the length BC.

3)    Strike an arc from the point B on the other side of the line.

4)    Without changing the compass setting strike an arc on the same side from the point C..

5)    Mark the point P where the arcs intersect.

6)    Draw a line m passing through A and P.

Line m is the perpendicular to the line l. Understanding 30 60 90 Triangles is always challenging for me but thanks to all math help websites to help me out.

Construct a Perpendicular – Proof

You will observe that, in both the cases the line m connects the points of intersections of circles of same radius. As per theorems on circles, the line m bisects the line l, joining their centers at right angle.

Variable Rate Calculator

Introduction to variable rate calculator:

The variable rate is defined as a rate of change in which it is expressed in the form of derivative. A calculator is a device that is used to perform arithmetic operations. The term rate can be calculated as the ratio of one thing or quantity to other. Also, the variable rate of any variables calculator with the help of a calculator. Here we discuss about the variable rate calculator.

Formula for Rate and Variable Rate of Change:

Rate:

It is a ratio in which the comparison of any two quantities can be done. It is calculated in a calculator in the form of proportion. In the calculator, it is calculated by the division operation. A rate can be found by dividing the distance with the time.

Variable rate of change:

The variable rate of change can be calculated as the change of rate value with any variables. The formula for variable rate is given as the change in variable of 'x' to the change in time.

Variable rate = `(dx)/(dt)`

Where,

dx is the change in variable

dt is the change in time.

Let us see about the calculator.

Calculator:

It is an important mathematical device which is used for calculation of all arithmetic operations.

In a calculator various symbols are there, they are used to do basic operations. For example, If we want to calculate the addition of 5 and 3 means, type the number 5 and then click the sign +. Now type the other number 3. Therefore the addition of two numbers is calculated as 8. I like to share this how to find the equation of a line with you all through my article.

Example Problem for Variable Rate Calculator:

We solve problem for calculating variable rate through calculator.

Problem for variable rate:

Calculate the variable rate of change with respect to variable x, for the given function f(x) = 6x2 + 4x.

Solution:

The given function is f(x) = 6x2 + 4x.

The formula for variable rate of change is (dx)/(dt).

So, we have to find the rate ofchange value of variable x in a calculator.

In calculator, the sign `d/dx` is used to find the rate of change.

Type the given function in calculator, then click the sign `d/dx`

Now the rate of change with respect to variable x is found or calculated as 12x + 4.

Hence the variable rate of change is calculated by a calculator.

These are about variable rate calculator.

Define Prime

Introduction to define prime

Normally the word prime is defined as “first, importance, greatest position, highest order, basics, and fundamentals”. In mathematics prime defines the prime number. Prime number is a whole number that is evenly divisible by 1 and the number itself. A natural number that has exactly two distinct divisors such as 1 and itself is called prime number (or simply a prime).There is infinity of prime numbers exist. The density of prime number compared to natural numbers is 0. The numbers 0 and 1 are not a prime number. Other than prime numbers are called composite numbers.

Calculation - Define Prime

How to calculate the prime numbers?

1 `->` The number is not a prime or composite.

2 `->` 1x2 = 2 and 2x1 =2. The number is divisible by 1 and itself (2), therefore this is even prime number.

3 `->` 1x3 = 3 and 3x1 = 3. The number is divisible by 1 and itself (3), therefore this is a prime number

4 `->` 1x4 = 4, 2x2 = 4 and 4x1 =4. The number is divisible by 1, 2 and itself (4), therefore this is a composite number.

5 `->` 1x5 = 5 and 5x1 =5. The number is divisible by 1 and itself (5), therefore this is a prime number.

6 `->` 1x6 =6, 2 x3=6, 3x2 =6 and 6 x 1 = 6. The number is divisible by 1, 2, 3 and itself (6). Therefore this is a composite number.

7 `->` 1x7 = 7 and 7x1= 7. The number is divisible by 1 and itself (7), therefore this is a prime number. I like to share this money math with you all through my article.

Example – Define Prime

Problem 1: Give the prime number from 10 to 20

Solution: Let us consider the values from 10 to 20 as

10 have divisors 1, 2, 5 and 10. This is composite number.

11 have divisors 1 and 11. This is prime number.

12 have divisors 1, 2,3,4,6 and 12. This is composite number.

13 have divisors 1 and 13. This is prime number.

14 have divisors 1, 2, 7 and 14. This is composite number.

15 have divisors 1, 3, 5 and 15. This is composite number.

16 have divisors 1,2,4,8 and 16. This is composite number.

17 have divisors 1 and 17. This is prime number.

18 have divisors 1, 2, 9 and 18. This is composite number.

19 have divisors 1 and 19. This is prime number.

20 have divisors 1, 2, 4,5,10 and 20. This is composite number

Venn Diagrams Finite Math Help

Introduction to venn diagram finite math help:-
Venn diagram  are diagrams that show all possible logical relations between a finite collection of sets. It is a collection of simple closed curves drawn on a plane. Sets are represented  by region.  There is a relation from one to the other.  Venn diagrams
comprise overlapping circles. The interior of the circle represent elements of the sets.  The exterior represent the elements that are not in the set.  The intersection of two circles contain the elements that belong to both the sets.

Venn Diagrams Finite Math Help with Images:

Venn diagram finite math help:-  Let us do a problem on the finite set A an B
Universal set ? = { 1,2,3,4,5,6,7,8}
Set A =  (1,2,5}
Set B = { 1,5, 8}
Represent these sets in a venn diagram This is a venn diagram where we can get finite math help.

We have represented the set A as yellow circle containing {1,2,5}  and the set B as green circle containing elements {1,5,8}
The elements {3,4,6,7} are outside the sets A and B.  The intersection of A and B contain elements {1,5}
Using the above venn diagram let us prove  ( A U B}'  =  A'nB'   This is De Morgan's law  for union of sets.
A U B =  {1,2,5,8}
(AUB)' =  ? - (AUB) =  {1,2,3,4,5,6,7,8} - {1,2,5,8} =  {3,4,6,7} ........ (1) ( Left hand side)
Now we must find A'   which is ? -  A = { 1,2,3,4,5,6,7,8} - {1,2,5} = {3,4,6,7,8}
Now let us find B'  which is ? - B = { 1,2,3,4,5,6,7,8} - {1,5,8} = {2,3,4,6,7}
Then we get A' n B' = { 3,4,6,7,8} n {2,3,4,6,7} = { 3,4,6,7} ............(2)(Right hand side)
Since (1) = (2) that is LHS = RHS we have proved that (AUB)'  = A' n B'. Is this topic free online math tutor hard for you? Watch out for my coming posts.

Venn Diagrams Finite Math Help with 3 Circles

Venn diagram finite math help can be used for a venn of three circles.
Now let us draw a 3 circle venn diagram.  Here we have A = {1,2,3,4,6} B = {2,3,4,7,8} C = {3,4,5,6,7} AnB = {2,3,4} BnC={3,4,7}  AnC = {3,4,6} and AnBnC = { 3,4}

This is a venn diagram with 3 circles,  Set A = { 1,2,3,4,6}   Set B = {2,3,4,7,8} and Set C = { 3,4,5,6,7}
Letus prove the De Morgan's law A - (BUC) = (A- B) n (A - C)
(BUC) = {2,3,4,5,6,7,8) {[ all the elements of B and C]
A - (BUC) =  { 1,2,3,4,6} - {2,3,4,5,6,7,8} = {1} .................(1)LHS
(A- B)  =  {1,2,3,4,6} - {2,3,4,7,8} = {1}
(A- C)  =  {1,2,3,4,6} - {3,4,5,6,7} = {1,2}
(A-B) n (A-C) = {1} n {1,2} = {1} .....................................(2) RHS
Since LHS = RHS we have proved the De Morgan's law
Venn diagram finite math help is very important because the diagrams help us to identify the  unions and intersections and
solve the problems very quickly.