Rhombus Definition Formula Calculation

A Rhombus is a quadrilateral with all four sides equal in length. Its a bit like a square that can lean over and the interior angles need not be 90 degree. Sometimes called a 'diamond' or 'lozenge' shape. A rhombus is a four-sided polygon in which every side has the same length. It is an equilateral quadrilateral.

Rhombus Formula :
Base Times Height Method : Area of Rhombus = b * h
Diagonal Method : Area of Rhombus = ½ * d1 * d2
Trigonometry Method : Area of Rhombus = a² * SinA
Perimeter of Rhombus = 4(a)
where
a = side, b = breadth, h = height, d1, d2 are diagonals

Rhombus Example :
Case 1: Find the area of a rhombus with the given base 3 and height 4 using Base Times Height Method.

Step 1: Find the area.
Area = b * h = 3 * 4 = 12.

Case 2: Find the area of a rhombus with the given diagonals 2, 4 using Diagonal Method.

Step 1: Find the area.
Area = ½ * d1 * d2 = 0.5 * 2 * 4 = 4.

Case 3: Find the area of a rhombus with the given side 2 using Trigonometry Method.

Step 1: Find the area.
Area = a² * SinA = 2² * Sin(33) = 4 * 1 = 4.

Case 4: Find the perimeter of a rhombus with the given side 2.

Step 1: Find the perimeter.
Perimeter = 4(a) = 4 * 2 = 8.

The above example will clearly illustrates how to calculate the Area, Perimeter of a Rhombus manually.

What is Abacus Maths?

The abacus is the best way to memorize tables in which children find themselves daunting. The abacus is the perfect tool for teaching the primary or high school students.

Abacus is a Latin word that has its origins in the Greek words abax or abacus (meaning "table" or "tablet") which in turn, possibly originated from the Semitic word abq, meaning "sand".

The "abacus system" of mental calculation is a system where users mentally visualize an abacus to do calculations. No physical abacus is used; only the answers are written down.

This system is being propagated in China, Singapore, South Korea, Thailand, Malaysia, and Japan. Mental calculation is said to improve mental capability, increases speed of response, memory power, and concentration power.

Many veteran and prolific abacus users in China, Japan, South Korea, and others who use the abacus daily, naturally tend to not use the abacus anymore but perform calculations by visualizing the abacus. This was verified when the right brain measured heightened EEG activity when calculating and compared with non-veterans who were using the abacus to perform calculations.

The standard abacus can be used to perform addition, subtraction, division, and multiplication; the abacus can also be used to extract square-roots and cubic roots.

Abacus Maths tutorial online

Performing Genius Addition on the Abacus
Addition on the abacus involves registering the numbers on the beads in the straight-forward left-to-right sequence they are written down in.
Additions
Addition on the abacus involves registering the numbers on the beads in the straight-forward left-to-right sequence they are written down in. As long as the digits are placed correctly, and the carry’s noted properly, the answer to the operation immediately presents itself right on the abacus.
There are 4 approaches to performing additions, each applied to a particular situation. Each of these techniques is explained in tabular form in the sections that follow.
Simple Additions
When performing the addition 6+2, one would move 1 bead from the upper deck down (value = 5) and one bead from the lower deck up (value = 1); this represents 6. Moving 2 beads from the lower deck (in the same column) up (value = 1 * 2 beads = 2) would complete the operation. The answer is then obtained by reading resultant bead positions.

Combined Adding-up And Taking Off
When the original number registered on a rod is smaller than 5, but will become greater than 5 after the addition, one bead from the upper-deck is moved down (added on to the beam) and one or more beads from the lower deck removed from the beam.
When a sum greater than 10 occurs on a certain rod, beads are removed from either or both the upper and lower decks and 1 bead is added to the rod directly to the left. Example: When adding 9 (10-1) to 8, one bead from the lower deck is removed (-1) and one bead from the lower deck on the row directly to the left is added (+10).

Combined Taking-off And Place Advancement
When a sum greater than 10 occurs on a certain rod, beads are removed from either or both the upper and lower decks and 1 bead is added to the rod directly to the left. Example: when adding 9 (10-1) to 8, one bead from the lower deck is removed (-1) and one bead from the lower deck on the row directly to the left is added (+10).

Combined Adding-up, Taking-off And Place Advancement
There are 4 cases when beads are added to the lower-deck, removed from the upper-deck and one bead added to the adjacent rod. Example: When adding 6 (+1-5+10) to 7, one bead is added to the lower-deck, one bead removed from the upper-deck and one bead is added to the left rod (lower-deck).

Performing Genius Subtraction on the Abacus
Subtraction is performed by first registering the minuend and then subtracting, starting from the left, by removing beads from either or both the lower or upper decks.
Genius Subtraction
Subtraction is performed by first registering the minuend and then subtracting, starting from the left, by removing beads from either or both the lower or upper decks. The final bead-positions represent the answer.
Simple Taking-off (Genius Principles)
This is achieved by simply taking off one or more beads from the lower deck, or sometimes both. Example: When subtracting 7 (represented by -5-2= -7) from 9, remove 1 bead from the upper-deck (-5) and 2 beads from the lower deck (-2). The remaining 2 beads represent the result.

Note: The “-” symbol in the Move bead(s) columns represents moving the bead(s) away from the middle beam.
Combined Adding-up And Taking Off (Genius Principles)
When the number of beads in the lower deck is less than the subtracter (the number being subtracted), one or more beads are added in the lower deck and 1 bead is removed from the upper-deck.
Example: When subtracting 4 (+1-5 = -4) from 7 (represented by 1 bead in the upper-deck and 2 beads in the lower deck (less than 4, the subtracter), one bead is added to the lower deck (+1) and 1 bead is removed from the upper-deck (-5) leaving 3 beads, representing the result.

Note: The “+” symbol in the Move bead(s) columns represents moving the bead(s) towards the middle beam; the “-” symbol indicates that the bead(s) should be moved away from the middle beam.

Taking-off From A Rod Of Higher Order And Adding-up (Genius Principles)
When a number on a specific rod is smaller than the subtrahend (4 is the subtrahend when performing 13 - 4; note that in the ones column, the 3 is less than the 4) one bead for the order of tens and one bead from the lower-deck has to be taken off, and one bead from the upper-deck is counted.

Combined Taking-off From A Rod Of Higher Order, Adding-up in the Upper-deck and Taking-off in the Lower-Deck (Genius Principles)
This technique is called for when a number on a specific rod is smaller than the supposed subtrahend [I have no idea what this means], but only in such cases as exemplified by 12 - 6.

What is Body Mass Index? BMI

Body Mass Index by definition is a statistical measure of the body fat scaled according to your ideal height and ideal weight. It has five categories which are listed in the table below.

Category BMI range
Starvation less than 15
Underweight from 15 to 18.5
Normal from 18.5 to 25
Overweight from 25 to 30
Obese greater than 30

Hence from the table BMI should always be less than 25.

BMI Formula:
Body mass index can be calculated in three units as SI, US and UK units.

SI Units:

BMI = weight(kg) / height²(m²)

US Units:

BMI = 703 X weight(lb) / height²(in²)
where,
1kg = 2.2lbs.
1cm = 0.39inches.

UK Units:

BMI = 6.35 X weight(kg) / height²(m²)

Example:

Consider a person's weight as 75kg and height as 157cm. Calculate BMI for the person.

SI Units = weight(kg) / height²(m²)
= 75 / (15.7)²
= 30kg/m²

US Units = 703 X (weight(lb) / height²(in²))
= 703 X ((75X2.2) / (157X0.39)²)
= 30lb/in²

UK Units = 6.35 X weight(kg) / height²(m²)
= 6.35 X (75 / (15.7)²)
= 193kg/m²

What is a Fraction? in Maths

By definition Fraction is the representation of a number in the form of a/b where a, b are whole numbers and b≠0.

Formula : a/b where b≠0
Example : 2/7 and 422/75

Break Even Analysis

Break Even = Fixed Cost / (Unit Price - Variable Unit Cost)

By inserting different prices into the formula, you will obtain a number of break even points, one for each possible price charged. If the firm changes the selling price for its product, from $2 to $2.30, in the example above, then it would have to sell only (1000/(2.3 - 0.6))= 589 units to break even, rather than 715.

To make the results clearer, they can be graphed. To do this, you draw the total cost curve (TC in the diagram) which shows the total cost associated with each possible level of output, the fixed cost curve (FC) which shows the costs that do not vary with output level, and finally the various total revenue lines (R1, R2, and R3) which show the total amount of revenue received at each output level, given the price you will be charging.

The break even points (A,B,C) are the points of intersection between the total cost curve (TC) and a total revenue curve (R1, R2, or R3). The break even quantity at each selling price can be read off the horizontal axis and the break even price at each selling price can be read off the vertical axis. The total cost, total revenue, and fixed cost curves can each be constructed with simple formulae. For example, the total revenue curve is simply the product of selling price times quantity for each output quantity. The data used in these formulae come either from accounting records or from various estimation techniques such as regression analysis.

Application

The break-even point is one of the simplest yet least used analytical tools in management. It helps to provide a dynamic view of the relationships between sales, costs and profits. A better understanding of break-even, for example, is expressing break-even sales as a percentage of actual sales—can give managers a chance to understand when to expect to break even (by linking the percent to when in the week/month this percent of sales might occur).

The break-even point is a special case of Target Income Sales, where Target Income is 0 (breaking even). This is very important for financial analysis.

Finger Multiplication of 6,7,8,9,10 Time Tables Trick to remember

Any easy way to remember multiplication of 6,7,8,9,10 Time Tables by fingers. This will help students to remember maths tables easily.

Place your fingers as in the below image and consider the value of fingers in each hand to be 6, 7, 8, 9 and 10 - in the order from small finger to thumb. 





Example 
Consider the multiplication of 7 × 8. 
Make the finger numbered 7 in the left hand to touch the finger numbered 8 in the right hand. 





Step 1: 
Now in the left hand, count the finger which is touching (7) and the ones below that = 2 fingers 
Similarly in the right hand, count the finger which is touching (8) and the ones below that = 3 fingers 
Add the above counted fingers = 2 + 3 = 5 fingers 
Multiply the number by 10 = 5 × 10 = 50 -----> (1) 

Step 2: 
In the left hand, count the fingers above the touching finger = 3 fingers 
Similarly in the right hand, count the fingers above the touching finger = 2 fingers 
Multiply both = 3 × 2 = 6 -----> (2) 

Step 3: 
Add (1) and (2), 
= 50 + 6 = 56 
So, the answer for 7 × 8 = 56 which is easily found through the above trick. 

Note: 
If there is no finger above the considered (touched) finger, then consider the value as zero (0). 

Play the same for the below multiplications
6 × 6 = ?	6 × 7 = ?	6 × 8 = ?	6 × 9 = ?	6 × 10 = ?
7 × 6 = ?	7 × 7 = ?	7 × 8 = ?	7 × 9 = ?	7 × 10 = ?
8 × 6 = ?	8 × 7 = ?	8 × 8 = ?	8 × 9 = ?	8 × 10 = ?
9 × 6 = ?	9 × 7 = ?	9 × 8 = ?	9 × 9 = ?	9 × 10 = ?
10 × 6 = ?	10 × 7 = ?	10 × 8 = ?	10 × 9 = ?	10 × 10 = ?