top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration Why to Join

    Get Free Puzzle Updates

Facebook Login
Site Registration

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?

0 votes
108 views

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?

Area of blue region

posted Jul 1, 2017 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button Google+ Share Button LinkedIn Share Button Multiple Social Share Button

1 Answer

0 votes

Size of highlighted area equal = 0.116 squr meter

answer Oct 9, 2017 by Emidway
What is the logic (please share the working)
Is it correct?!
Trying to send photo of paper can’t ... and it’s horrible lol
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
cool superb...



Similar Puzzles
+2 votes

In the figure, if ABCD and EFGC are squares with areas R and S respectively. What is the area of the blue region?

Area of Blue region

0 votes

In the figure square ABCD is inscribed in a circle. EFGH is also a square with points E, F on circle and G, H on side of bigger square.
Find the ratio of the areas of the bigger square to the smaller square?

enter image description here

0 votes

Following figures shows a unit square ABCD. If the area of the octagon (in blue) can be expressed as 1/a find a?

enter image description here

+3 votes

ABCD is a square of side length 1.

If EFGH are the points on its boundary such that AE=EB, 2BF=FC, 3CG=GD & 4DH=HA then what is the area of the quadrilateral EFGH?

enter image description here

Contact Us
+91 9880187415
sales@queryhome.net
support@queryhome.net
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Bangalore-560102
Karnataka INDIA.
QUERY HOME
...