refer to the diagram attached..
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first find the area of CBD...pir2/4 = 3.14/4 = 0.785
now, the area in peach is = y; the green area = x
total area of square = 1
square comprises of 4 peach shaded region + 4 green shaded region + 1 z
= 4y + 4x + z =1 (1)
CBD = 0.785
therefore, the area of the remaining part = 1 - 0.785 = 0.215
this area comprises of 2 peach shaded region + 1 green shaded region = 2y + x = 0.215
rearrange => y=(0.215 - x)/2
put this value of 'y' in the (1) equation
7x + 2z = 1.785 (keep this equation in mind)
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now consider the sector CBD
area = 0.785
it comprises of 3 green + 2 peach + 1 z
3x + 2y + z = 0.785
substitute 'y' value here
y = (0.215 - x)/2
so that gives us...
2x + z = 0.57
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now for the final sim. equations
7x + 2z = 1.785
2x + z = 0.57 (*2)
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7x + 2z = 1.785 (subtract them)
4x + 2z = 1.14
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3x = 0.645
x = 0.215
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substitute in any equation to find the value of z
lets use 2x + z = 0.57
(2*0.215) + z = 0.57
z = 0.57 - 0.43
z = 0.14
done!
Adi, the right answer goes like this.
first of all you need to eliminate the Pink portion in Fig 1. which is very simple, u have already done it.
Now we are left with the middle 'eye' like structure.(brown and white portion).
next we note that the angles in Fig 2 are always the same, 30 deg each.
now we find the yellow portion in Fig 3. by finding the area of the sector with the formula 0.5(r)
2theta.
and subtract the area of the triangle. then u r left with yellow portion.
now double the area of yellow portion and you cover the following yellow area's. in Fig 4.
next we need to find the green portion which is simple again. sector formula for 30 deg.
now u add the area's of the green and yellow portion.
at this point of time you might observe you are left with white potion marked 'A' in Fig 4.
you can find this by subtracting the area found in Fig 4. from the area of the eye shape.
now twice the area of 'A' you will get the area of the light blue portion in Fig 5.
finally subtract it with the area of the eye shape again.
you will get the area of brown. which when solved is 0.31 squared units.
i Hope this was clear.