Geometry Area Problems

Introduction :

In this article we are going to study geometry areas Area is region covered by two dimensional shapes. Based on the shape of the area we can drive the area formula of the shape. Based on the shape properties we have some formulas in below. In this section we will see brief about area of different shapes such as square, trapezoidal, square, triangles, cone, circle, parallelogram, and so on. Here we have some sample solved problems of area in geometry. Some important area formulas are listed in below sub topics. Area is amount of gap within a particular closed boundary. There are different measures to calculate the area in geometry. Now we are going to solve some area problems in geometry using the following area formulas.


Some area formulas in geometry:


In below we have some of the area formulas in geometry:

Square:

Area of the square = a *a square units

Where, a is a side of the square

Rectangle:

Area of the rectangle = l * b square units

Where, l and b is length and breadth of the rectangle with respective.

Circle:

Area of the circle = `pi ` * r2 square units

Where, r is a radius of the circle.

Triangle:

Area of the triangle = `1/2` b * h square units

Where, b is breadth and h is height of the triangle.

Trapezoidal:

Area of the trapezoidal = `1/2` * a * (b1 + b2) square units

Where, a is side length of trapezoidal , b1 is base1 and b2 is base2 of the trapezoidal.

Parallelogram:

Area of the parallelogram = b * h square units

Where, b is base and h is perpendicular height. I have recently faced lot of problem while learning Bisector of a Triangle, But thank to online resources of math which helped me to learn myself easily on net.


Some example problems using the above area formulas in geometry:

Problem 1: Can you calculate the area of a parallelogram with a base of 5 inches and a height of 8 inches.

Solution:

Given: base is 5 inches and height is 8 inches.

We know that,

Area of the parallelogram = b * h square units

Area of the parallelogram = 5 * 8 = 40 square inches.

Therefore, the area of the parallelogram is 40 square inches.

Answer: The area of the parallelogram is 40 square inches.

Problem 2: The school park has a circular pond with a diameter of 6 feet. What is the pond's area?

Solution:

Given: d = 6 feet.

Therefore, radius = `6/2 ` = 3 feet

Area of the circle = p r2 square units.

The diameter is 6 feet. Replace d by 6 in the formula.

Area = p * 3 * 3 = 3.14 * 9 = 28.26 square units.

The area of the circle is 28.26 square feet.

Answer: The area of the circle is 28.26 square feet.

One more example problem using the above area formulas in geometry:

Problem: A square playground has an area of 100 square meters. How long is each side?

Solution:

The area of a square is the side length times itself.

Consider of a number that, when multiplied by itself, gives 100:

10 × 10 = 100

Each side is 10 meters long.

Answer: Each side is 10 meters long.

Fractions Solving Online

Introduction :
DEFINITION:

Fraction is defined as an equal amount of one whole object. It can be represented as " a / b " where 'a' denotes the value called numerator and 'b' denotes the value called denominator and q not equal to zero.we can  easily perform these operations online

The fundamental rule of fractions is given as follows:

Multiplying both numerator and denominator by the same number because it does not change the value of the fraction. It is one of the most important steps used in dealing with equaling the fractions.by doing problems online we can quickly get the answers.


Description about fractions solving online:


Adding fractions:

There are 3 Simple Steps for solving the addition fractions:

Step 1: Make sure the bottom of the numbers that is denominators are the same or not

Step 2: Add the top numbers (the numerators). Put the answer over the same denominator as in step 1

Step 3: Simplify the fraction (if needed)

Ex:

1 / 4 + 1 / 4

Step1. The bottom numbers are already the same. Go straight to step 2.

Step2. Add the numerator and put the answer over the same denominator:

1 / 4 + 1 / 4 = (1+1) / 4 = 2 / 4

Step3. Simplify the fraction:

2 / 4 = 1 / 2

Subtracting Fractions:

There are 3 simple steps  for solving subtract fractions:

Step1 Make sure the bottom numbers (the denominators) are the same or not

Step2 Subtract the top numbers (the numerators). Put the answer over the same denominator.

Step3 Simplify the fraction.

Ex:

3 / 4 – 1 / 4

Step1 The bottom numbers are already the same. Go straight to step 2.

Step2 Then subtract the numerator and substitute the answer over the same denominator:

(3 / 4) - (1 / 4) = (3 - 1) / 4 = 2 / 4

Step3 Simplify the fraction:

2 / 4 = 1 / 2

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Practice problems for fractions solving online

Multiplying Fractions:

There are 3 simple steps to multiply fractions:

Step1 Multiply the top numbers (the numerators).

Step2 Multiply the bottom numbers (the denominators).

Step3 Simplify the fraction if needed.

Ex:

1 / 2 * 2 / 5

Step1. Multiply the top numbers:

1 / 2 * 2 / 5 = 1 * 2 / = 2 /

Step2. Multiply the bottom numbers:

1 / 2 * 2 / 5 = (1 * 2) / (2 * 5) = 2 / 10

Step3. Simplify the fraction:

2 / 10 = 1 / 5

Dividing Fractions:

There are 3 Simple Steps to Divide Fractions:

Step1 Turn the second fraction into as a reciprocal of itself.

Step2 Multiply the first fraction by that reciprocal

Step3 Simplify the fraction (if needed)

Ex :

(1 / 2) / (1 / 6)

Step1 Turn the second fraction upside-down (the reciprocal):

1 / 6 = 6 / 1

Step2 Multiply the first fraction by that reciprocal:

(1 / 2) * (6 / 1) = ((1 * 6) / (2 * 1)) = 6 / 2

Step3 Simplify the fraction:

6 / 2 = 3

Check a Solution Online

Introduction to check a solution online:

In mathematics, check means the process of confirming a solution is correct or not for the given equation or inequality. Check is nothing but substitute the solution in the given question. Now, we are going to see some of the problems to check the solution online. From these problems, we can get clear view about whether the solution is correct or not for the given question. Is this topic online geometry tutor free hard for you? Watch out for my coming posts.


Problem on check a solution online:


Example problem 1:

Solve for x in the given equation and check the solution online: 5 x - 6 = 3 x - 10

Solution:

Subtract 3x on both sides of the equation

5 x - 6 = 3 x – 10

Add 6 to both sides of the equation

5 x - 6 + 6 = 3 x – 10 + 6

5x = 3x – 4

Subtract 3x on both sides of the equation

5x – 3x = 3x – 4 -3x

2x = -4

Divide by 2 on both sides of the equation

2x / 2 = -4 / 2

x = -2

The answer is x = - 2

Check:

Substitute the value x = -2 in the given equation

5 x - 6 = 3 x – 10

5 (-2) - 6 = 3(-2) – 10

-10 – 6 = -6 – 10

-16 = -16

Both the sides are equal. So, the answer is correct. I have recently faced lot of problem while learning Large Sample Size, But thank to online resources of math which helped me to learn myself easily on net.


Additional Problem on check a solution online:


Example problem 2:

Solve the simultaneous equations and check the answer:

x + y = -1-----------Equation (1)
2x + y = 0-----------Equation (2)

Solution:

Step 1: From equation (1)

x + y = -1

Subtract x on both sides of the equation

x + y – x = -1 – x

y = -x – 1----------Equation (3)

Step 2: Substitute the equation (3) in equation (2)

2x + y = 0

2x + (-x – 1) = 0

2x –x – 1 = 0

x – 1 =0

Add 1 on both sides of the equation

x – 1 + 1 = 0 + 1

x = 1

Step 3: Substitute x=1 in equation (3)

y = -x – 1

y = - 1 – 1

y = -2

So, the solution is (1, -2)

Verify:

Substitute the x and y values in any one of given equation

Let us take equation (1)

x + y = -1

1 + (-2) = - 1

-1 = -1

Both the sides are equal. So, the answer is correct.

Define Associative

Introduction to algebra:

Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures. Together with geometry, analysis, topology, combinatorics, and number theory, algebra is one of the main branches of pure mathematics. Please express your views of this topic Factor Polynomial Calculator by commenting on blog.

Source:  Wikipedia


Concept of associative property in algebra:


The associative property in algebra also works for addition and multiplication. For addition, the associative property in algebra means that when you add three numbers, you can first add any two of the numbers and then add the third.

Associative property for addition in algebra:

First, add any two of the numbers and then add the third.

(p+q)+r=p+(q+r)

The parentheses group numbers together. Suppose you want to add 1+2+3. You could first add 1 and 2 to get 3, and then add 3 and 3 to get 6. Or you could first add 3 and 2 to get 5, and then add 5 and 1 to get 6. The results are the same in algebra addition.

If you replace p with 1, q with 2 and r with 3, the associative property in algebra of addition looks like this:

(a+b)+c=a+(b+c)

(1+2)+3=1+(2+3)

3+3=1+5

6=6

Associative property for multiplication in algebra:

First, multiply two numbers and then multiply that product by the third number.

(p*q)*r=p*(q*r) or (pq)r=p(qr)

Again, the parentheses group numbers together. Suppose you want to solve the multiplication problem 1x2x3. You could first multiply 1x2 to get 2, and then multiply 2x3 to get 6. Or you could first multiply 2x3 to get 6, and then multiply 6x1 to get 6. The results are the same.

If you replace p with 1, q with 2, and r with 3, the associative property in algebra of multiplication looks like this:

(pq)r=p(qr)

(1*2)*3=1*(2*3)

2*3=1*6

6=6

Example for associative property in algebra:

Example 1:

Which of the following is the same as (10+12)+15?

10(12+15)

(10+12)15

10+15+12+15

10+(12+15)

Solution:

Answer (4) is the correct choice. You could first add 10 and 12 to get 22, and then add 22 and 15 to get 37. Or, you could first add 12 and 15 to get 27, and then add 10 and 27 to get 37.

Example 2:

Which of the following is the same as (5x2)x3?

5(2+3)

(3+2)5

5x2+5x3

3(5x2)

Solution:

Answer (4) is the correct choice. You could first multiply 5 and 2 to get 10, and then multiply 10 and 3 to get 30. Or, you could first multiply 2 and 3 to get 6, and then multiply 6 and 5 to get 30. Is this topic algebra 2 homework solver hard for you? Watch out for my coming posts.


Practice problem for associative:


Problem 1:

Which of the following is the same as (8+2)+5?

8(2+5)

(8+2)5

8+5+2+5

8+(2+5)

Answer: 4.

Problem 2:

Which of the following is the same as (5+2)*6?

5(2+6)

(5+6)2

(5*6)+(2*6)

(5+6)+2+15

Answer: 3.

Problem 3:

Which of the following is the same as (5*2)+6?

6+(2*5)

(5+6)2

(5*6)+(2*6)

(5+6)+2

Answer: 1.

What is Coefficient of Variance

Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.

The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:

Whenever we want to compare the variability of two series which differ widely in their averages or which are measured in different units, we do not merely calculate the measures of dispersions but we calculate the coefficients of dispersion which are pure numbers independent of the units of measurement.

The coefficients of dispersion (C.D.) based on different measures of dispersion are as follows:

1.  C.D. based upon range = `(L-S)/(L+S)`  , where L and S are Largest and Smallest observation in the series.

2.  C.D. based upon quartile deviation = `(Q3 - Q1)/(Q3 + Q1)`

`3. `C.D. based upon Standard deviation = `sigma/barx`


Definition of Coefficient of Variance


Coefficient of variance i.e. Coefficient of Variation is a relative measure for standard deviation. It is defined as 100 times the coefficient of dispersion based upon standard deviation is called coefficient of variation (C.V.), i.e.,

C.V.  =  `sigma/barx` x 100 .

Since it is relative measure C.V. is used to compare consistency of figures or variability of figures.

Remarks:

1. Less C.V. indicate the less variability or more consistency.

2. More C.V. indicate the more variability or less consistency.

3. According to Karl Pearson who suggested this measure, C.V. is the percentage variation in the mean, standard deviation being considered as the total variation in the mean.

Note:

With the help of C.V. we can find which salesman is more consistent in making sales, which batsman is more consistent in scoring runs, which student is more consistent in scoring marks, which worker is more consistent in production, etc.

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Example of coefficient of variance


An analysis of monthly wages paid to the workers of two firms A and B belonging to the same industry gives the following results:


Firm A
Firm B
Number of workers
500
Average daily wages
186 Rs.
175 Rs.
S.D. of daily wages
9    10
In which firm, A or B is more consistent in individual wages?

Solution:

C. V. for firm A  = `sigma/barx`` x 100 = 9/186 x 100`

` = 4.84`

C. V. for firm B  = `sigma/barx`` x 100 = 10/175 x 100`

` = 5.71`

`Since C.V. for firm B is greater than C.V. for firm A, firm A is more consistent.`

Answers For Parentheses

Introduction :

Parentheses are defined as the process of the symbols “(” and “)”. It can be generally used in grouping. Different types of parentheses are "[ ]”, " ","( )". These three types of parentheses are called as round brackets, curved brackets and oval brackets or just brackets. It can be used to mention the modifications of normal order of operations. Parenthesis is the single type of parentheses.


Example problems for answers for parentheses:

Some example problems for answers for parentheses are

Example 1:

Given:

(8+5) * (7-3)

Solution:

Step 1:

First we need to simplify the parenthesis

Step 2:

So, (8+5) = 13 and (7-3) = 4.

Step 3:

Now we have 13 * 4 = 52.

Solution to the problem is 52

Example 2:

Given:

(28+4) -5.

Solution:

Step 1:

First we need to simplify the parenthesis so,

Step 2:

(28+4) = 32.

Step 3:

Now we need to subtract 5 from 32.

Step 4:

so we get 32 -5 =27.

Solution to the problem is 27.

Example 3:

Given:

6+ (4+2).

Solution:

Step 1:

Here first we need to simplify (4+2) =6.

Step 2:

Now we need 6 with 6.

Step 3:

6+ (6) the answer is 12.

Solution to the problem is 12.

Example 4:

Given:

2x + 4xy + 5x (y + z).

Solution:

Step 1:

From this question, first we need to simplify the brackets so,

Step 2:

we multiply (y + z) with 5x. So we get 5xy +5xz.

Step 3:

Now we have 2x + 4xy + 5xy + 5xz.

Step 4:

When we add like terms we get 2x + 9xy + 5xz.

Solution to the problem is 2x + 9xy + 5xz.

Example 5:

Given:

(5*12) +11+36.

Solution:

Step 1:

First we need to simplify the parenthesis, So (5*12) = 60.

Step 2:

Now we can add 11 and 36 with 60.

Step 3:

60 + 11 + 36

Solution to the problem is 107. Understanding Decimal to Fraction Converter is always challenging for me but thanks to all math help websites to help me out.


Practice problems for answers for parentheses:

Some practice problems for answers for parentheses are

1. Simplify the parentheses (52 +12) - (12 + 10)

Answer to the problem is 40.

2. Simplify the parentheses (5 + 3) × (2 + 8)

Answer to the problem is 128.

Live Online Math Tutoring

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Tutorvista.com is one such live online tutoring company providing 24/7, 365 days service with well qualified math tutors.It is so easy to access live online math tutors from anywhere you wish, as it does not require unwieldy software's and plug-ins, it is easily accessible from any computer with Internet access.


Uses of live online tutoring


Online live math tutoring gives you a very personal tie up with the live tutor, it's only you and the tutor and no one else to interfere.  You can learn any topic,clarify any doubts with utmost ease with the use of live chat and interactive whiteboard. Any kind of questions can be asked in live sessions which is not at all possible sometimes in your class room or home tutoring as you may feel guilty and think that would be a silly question.

In live online math tutoring as you do not come face to face with the tutor you feel safe and gaurded and only in online live math tutoring you can abruptly get away from the session if you feel like the live session is of no help which is not possible while learning in class room or home.


Why live online tutoring?


It's so simple at the current scenario as most of the households have computer and Internet connection. Live online math tutoring is mostly available round the clock so accessing a tutor any time from any where is only possible with live online tutoring as all other learning media have time constraints like schools or colleges have specific timings,home tutors visit only at certain time and day.It is hygienic as you do not come in direct contact with the tutor.

Live online math tutoring requires a computer with Internet access and the interest to learn live online.After all math is an universal language.