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28 Nov 2009, 04:18
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A square of side 2 cms (1+1) is given. Find the area of the shaded region?
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28 Nov 2009, 06:33
The area of each of the colored triangle is 1/2*1/2*1 =1/4

There are four such triangles so total area of the colored region is 1
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28 Nov 2009, 11:14
nope buddy,
how can you prove that base of triangle is 1/2 ???
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28 Nov 2009, 14:44
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Consider Right tri'gle HFC. We have to figure out if R is mid-point of OG.

Two right tri'gles HFC and HOR are similar triangles by angle-side-angle (asa) property.
1) Angle RHO is same as Angle CHF.
2) HO and HF are in straight line, given that O is mid-point of HF, HO/HF = 1/2.
3) Angle HOR is same as Angle HFC = 90 degree.

So HO/HF = HR / HC = OR / FC = 1/2.
Hence, OR is half of FC. And OG = FC = 1. Therefore, R is mid-point of OG.

You can take it from here.
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28 Nov 2009, 19:59
brothers wrote:
nope buddy,
how can you prove that base of triangle is 1/2 ???

And also, as Square HOGD and Square OGSF are congruent and occupy exactly half the area of the rectangle HDFC. The diagonal HC cuts OG exactly at the mid point.
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