Question

If ABCD is a square of area 1. E, F are mid points of AB and BC respectively. What is the area of blue region?

Answer 1

Size of highlighted area equal = 0.116 squr meter

Comments

What is the logic (please share the working)

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Is it correct?!
Trying to send photo of paper can’t ... and it’s horrible lol

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Ok here is my logic
But if your confused ( I know !!! Loool )

The logic in solving the question
The information that I have is that the square ABCD = 1 m Sqr
Which makes each line in the squr = 1
And that the points F and E are the exact middle of lines CB , AB respectively
Please note :
(^ )means triangle and (< ) means angle
First I took
^ FBE which I have < B = 90 and line AB = 1 abd line FB=0.5

To find FE^2 = FB^2 + AB^2
                       = 1+0.25 = 1.25
                FE= 1.118

Tan^-1 (<A)= FB/AB 0.5 /1 = 0.5
Tan^-1(<A) = 26.565

<F = 63.435

Area of ^FBE = 0.25
(I know that this is long I could’ve divided the square from point E to its opposite side on which would give me an area of 0.5 and blah blah blah divide by two =0.25 but I needed the angles of f and A )

Ok then I took ^ BCD similar calculation
Given BC= 1 CD=1 < C = 90
Result
< B = 45  < D = 45
Line DB = 1.414

 Please note that point G is the cross section between the lines AF and DB
 And point H is the cross section of Af and De

3rd ^ BGF
Given BF=0.5 <F 63.435 ( from first calculation) <B 45
Then < G = 71.565 logic (180-<F+<B in ^ BGF)
Calculation line GF= 0.373 line GB = 0.373
Area = 0.069
Note I drew a line from point E to <C going through point G
4th ^ BEG  given ( line BG=0.373 line BE=0.5 <B = 45 from ^ BCD <B= 45 {90-45=45}

Result line EG=0.373 <E= 63.376 < G =71.624
Area of ^BEG=0.083
 5th triangle ^ AEB given line Eb= 0.5 line BD=1.414 from 2nd calculation angle B=45 ( 90-45 )
Result
<D=18.433 <E=116.562 line DE=1.118


Final ^ EHG given (from 3rd and 4th triangles <G = 71.565 , <G 71.624 - 180 line AF =36.811 ) so < G in triangle EHG= 36.811 )
From fifth triangle < E = 116.562 subtract <E from ^ EGB WHICH IS 63.376 result =53.186 and line EG= 0.373 ) and finally <G found it from subtracting 180(line FA ) - < G from ^ BGf 3rd triangle = 71. 565 and <G from 4th triangle = 71.624
{180-71.565+71.624= 36.811 }
So < G in triangle EHG = 36.811
We calculate final triangle ASA
Result
Area of ^ EHG =0.033

Result = Area of ^BEG=0.083 + Area of ^EHG =0.033

Area BHGB = 0.116

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cool superb...