Well, as I am preparing for CAT 2012, so i thought it would be nice to share some out of the box things which i learn at my coaching classes. This might help you somewhere, and will be saved as an archive for my reference also. There is something very special kind of geometry I learned last week, and I am now exploring all the application part. The concept is very simple, and can be applied to any problem. Here is how I can explain it-

__The concept-__

It uses very simple principle of physics, which we have often observed in our daily life, see the figure below

__An Example-__

Question : – Consider the case below here are of small triangles contained in big triangle are known, now we have to find the area of whole triangle, I bet you can’t do this question in less than 10 minutes if you don’t know this method. Give it a try if you want to, before reading the solution.

Answer : – As we know base of triangle is in the same ratio as the areas are, when a line cuts triangle, hence the ratio of base will be same as ratio of areas.. Therefore, ratio of base-

Now, using mass geometry i can complete this triangle as shown below-

Here, numbers written are nothing but ratios of sides, we know the area and ratio of sides. Therefore, we can find unknown area of quadrilateral. Picture below shows the actual areas in squares and ratios of sides. Using this we can say that, ratio of area of triangle ABE and triangle BCE = (4+x)/(8+13) = 7/1, where x is area of quadrilateral.