Area Displacement Theory

.
Maths is not all about calculation.

There are always more to it than meet the eyes.

This is especially true when you are doing geometrical questions where you are involved with area, perimeter and so on.

Displacement theory or its equivalent is always done without the knowledge of many people.

What is this theory about?

Let's look at one example below.

In the diagram above, you will see a path (white coloured) going across a blue platform.
If you are asked to find the area of this path, what can you do to obtain this area?

If no data of dimension is given, it is definitely not possible.

Now if the width of the path and the vertical length of the blue platform is given, can you compute the answer?

Again , this need a bit of thinking.

Displacement theory kicks in here. Look at the diagram on the right.

It is the displaced or closed up portion of the blue platform that does the trick.
Here you will notice the dashed line forming a white rectangluar area on the right-most side of the white blue platform.

Are you able to find the area of this white rectangular piece?
The width of this rectangle piece is ACTUAL the width of the white path!

You should now be able to calculate the area of this rectangular piece since the path width and length of the rectangular block is known or deduced now.

How this is possibe is through the "hidden" clue or step of closing up the path revealing the simpler rectangular area that any decent maths student can calculate.

Hence, maths is wonderful in that it tests you not only about applcations of maths tools, but your other "intelligence".

Having known displacement theory here, I believe you are really for the Math Challenge 23.
Go there and answer the question, and be quick before others grap the position one ... 

:-D
.