Percentage Increase in Area

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Is there any formula or maths expression showing the ncrease in area when its length and its breadth are increase by m% ?

If you cannot find one, it does not matter. You can easily derive one!

Let us work on this and show the others how simple maths can help us solve daily issue.

Let the length be x and breadth be y.

If x and y increase by m%,
length becomes x + x(m/100), and breadth becomes y + y(m/100).

Area is length x breadth.

Thus new area becomes  [ x + x(m/100)] [ y + y(m/100)]

This gives us an area of  xy + (m/100)xy + (m/100)xy + (m/100)(m/100)xy.

From the above maths expression, we can deduce that increase in area is:
2 x m%  +  (m%  x  m%)/100

Example with numbers will convince readers better, therefore ......

Example

If the increase in perimeter is 10%, what is the increase in area?

Answer is 2 (10%)  + (10%  x  10%)  /100  = 20%  +  1%  = 21%

Easy isn't it? 

For other post related to this concept in percentage increase, see the post Percentage Increase in Perimeter.

Maths is interesting. 

;-D

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Percentage Increase in Perimeter

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Percentage is a nice and mystery word in maths.

Why do I say that?

Look at the example below:

If the perimeter has increased by 30%, does the length also increases by the same amount?

The answer is obviously YES.

Next,

If the perimeter is increased by 30%, does the area covered by it also increases by the same amount?

???  The answer needs some pondering, right?

Answer to this:
If the perimeter is increased by 30%, the length and width will both increase by 30%.
This makes the area increase by 2(30%) + (30% x 30%) = ?

(I will explain this maths calculation in a later  post.)
For now, let's concentrate on the maths operation.

What do you get from 30% x 30%?
30% = 0.3
Thus 30% x 30% = 0.3 x 0.3 = 0.09 = 9%

This is a potential mathematical  mistake.
Error:  30% x 30% = 900% !

So, increase in area becomes 60% + 9% = 69%

Interesting how the mind works.

If the mind is not clear when doing maths, common mistakes do occur.
With more practice, however, this form of mistakes will be lesser.

Hence, be careful when dealing with parameter such as perimeter, length and AREA.
Know their relation and be aware of the "catch" when this type of maths question is being asked.

Do not fall for the maths trick.

:-)
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Hidden Clues in Maths Questions

There are different levels in any educational system.
This goes with the learning of mathematics too.

At various level of learning, you will be presented with different level of complexity.

At the elementary stage, you will be shown maths questions that are real straight forward type.
At intermediate, a bit of mind twisting has to be done to resolve any challenge.
At the highest level, the questions come embedded with hidden clues to be discovered by learners and used to continue with the solving process.

But hidden clues are now becoming the norm among intermediate level due to its benefits to prevent pure memorising of mathematical technique.

A example of this interesting "hidden clue" can be seen in my Math Challenge 23.

There anyone taking up the challenge needs another step in order to "see" through the simple trick of solving the issue.
(Note:  The challenge requires only one step to calculate the area of the path).

Multi-discipline is thus needed for merit of helping get the answer.
Knowledge in utilising maths tools and technique are not sufficient these days.

Maths students have to know some basic theory of motional replacement to understand Math Challenge 23.


Hence, to master mathematics, it will be good to read more, especially, topics outside maths.
This enlarge your understanding of real-life cases roped into maths questions.
 
Maths is interesting in this manner since it involves not only one learning discipline but encompasses more.
 
Enjoy maths. It widens your perspective of the world. 
 
:-)

Math Challenge 23

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Albert needed to create a path through a garden of his.

The garden has a size of a rectangle with length of 20m and width of 15m.

He intend to have a path of 3m wide.

His design is shown below.

But he has a problem.

He wanted to know what is the area of this path he is going to lay across the garden.

Can anyone help him calculate that area?

Basic geometry knowledge may helps.

Math Challenge 22

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Given the diagram of boxes below, determine, in the fastest possible way, the area of the dark blue region.

Assume the individual boxes to be 1 unit square in area.

Give your answer in the comment space, please.

Maths does not involve plain counting.

It involves some form of intelligence to get things going.

:-)

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Artistic Mathematical Lantern

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Have you wondered what can maths do to art?


Below is a lantern made by a mathematical expression.

With maths, you can be assured of producing wonderful images when you have the appropriate expression.


Do create some for enjoyment.


Maths is interesting.


:-)