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tough nut of geometry
by Rohit Mishra - Wednesday, 12 November 2014, 02:05 PM
 
Hi
     In the figure attached, find the ratio of the area of the shaded figure to area of the rectangle by mass point geometry. the points on the sides are mid points. Ignore the rest of the data and the question.

Re: tough nut of geometry
by TG Team - Wednesday, 12 November 2014, 02:48 PM
 
Hi Rohit smile

I don't see any need and any way to use Mass-Point concept here. It's a very basic question and can be solved very easily with basic geometry concepts.

See in the below diagram, as the points on two mutually perpendicular sides are mid points of those respective sides, we get to know that

(3 + x + 20) + (2 + y) = Half of area of rectangle {as the remaining triangle has same base and height as that of rectangle and hence have half of area of rectangle}

Also, with same logic as above (x + Shaded Area + y) = Half of area of rectangle.

Of course two halves of same area are equal, so equating them we get:

(3 + x + 20) + (2 + y) = (x + Shaded Area + y)

i.e. Shaded Area = 3 + 20 + 2 = 25. smile

Kamal Lohia

Re: tough nut of geometry
by Rohit Mishra - Wednesday, 12 November 2014, 06:30 PM
  The question is what I have written, not what is written in figure- I have told to ignore all that is written in the figure and only consider the diagram!!!!!!!!