Wednesday, 24 March 2010

Percentage Increase in Area

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 ......


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. 



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