Post by: nid404 on October 01, 2009, 03:48:32 pm
the quadrilateral is a square
Find the area of the shaded region
note-the four shapes touching the vertices are not triangles.....i couldn't draw it perfectly
thanks :)
Post by: Ghost Of Highbury on October 01, 2009, 06:01:29 pm
ekdum jhakaas~~
:P..will try
Post by: Ghost Of Highbury on October 01, 2009, 06:02:56 pm
are they a sector ???
Post by: nid404 on October 01, 2009, 06:04:59 pm
wait i'll try and make the drawing better
Post by: nid404 on October 01, 2009, 06:19:15 pm
oh the sides are of 1 unit....i think i mentioned it before
please help me answer it
Post by: astarmathsandphysics on October 01, 2009, 06:39:06 pm
The whole area =4x+y+4z=1
Put a compass on the corner of the square and form part (1/4) of a circle. The area of that part is 3x+y+2z=
TDo this again but on the opposite side of the square to obtain another quarter of a ficle. The difference beween these two quarters and the area of the square istwo triangles and the middle from diagonal to diagonal ie 2x+y=
Solve these equations simultaneously.
Will try and finish it when I get home in a few hours
Post by: nid404 on October 01, 2009, 06:45:44 pm
@astar-they r not triangles is what i am specifically told by the teacher.....
Post by: astarmathsandphysics on October 01, 2009, 06:53:40 pm
Post by: nid404 on October 01, 2009, 07:03:59 pm
when you get back home, could you do it with the diagram please??
Post by: Ghost Of Highbury on October 01, 2009, 07:23:32 pm
.
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)
----------------------------------
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
--
now for the final sim. equations
7x + 2z = 1.785
2x + z = 0.57 (*2)
--------------------
7x + 2z = 1.785 (subtract them)
4x + 2z = 1.14
-----------------
3x = 0.645
x = 0.215
------------
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!
Post by: Ghost Of Highbury on October 01, 2009, 07:50:53 pm
Post by: nid404 on October 02, 2009, 05:23:13 am
I don't know the answer....it's just a challenging question that our teacher gave us(IIT)
I did another method and got 0.136.....so I guess that is right too
Post by: Ghost Of Highbury on October 02, 2009, 05:26:49 am
Post by: Ghost Of Highbury on October 02, 2009, 12:03:15 pm
Post by: nid404 on October 02, 2009, 12:03:44 pm
Post by: nid404 on October 02, 2009, 12:04:17 pm
Post by: Ghost Of Highbury on October 02, 2009, 12:08:13 pm
Post by: nid404 on October 02, 2009, 12:19:06 pm
Post by: Ghost Of Highbury on October 02, 2009, 07:29:47 pm
Post by: Eamyzz on October 07, 2009, 04:58:05 pm
Post by: Eamyzz on October 08, 2009, 12:46:27 am
Post by: Ghost Of Highbury on October 08, 2009, 05:59:27 am
heres the i) find dy/dx => let u=6 ; v= 3x-2
therefore => du/dx = 0 and dv/dx = 3
dy/dx = (vdu - udv)/v2 => (-18)/(3x-2)2
apply x =2 in dy/dx
u get
-18/16 = -1.125/
Post by: astarmathsandphysics on October 08, 2009, 04:08:28 pm
Post by: sameer210394 on October 16, 2009, 12:05:27 am
refer to the diagram attached..
.
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)
----------------------------------
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
--
now for the final sim. equations
7x + 2z = 1.785
2x + z = 0.57 (*2)
--------------------
7x + 2z = 1.785 (subtract them)
4x + 2z = 1.14
-----------------
3x = 0.645
x = 0.215
------------
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!
Abbey Mallu, I solved the same question with sumit in our free period, lolz...
remember we had done these types of sums.
Post by: sameer210394 on October 16, 2009, 06:19:17 am
refer to the diagram attached..
.
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)
----------------------------------
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
--
now for the final sim. equations
7x + 2z = 1.785
2x + z = 0.57 (*2)
--------------------
7x + 2z = 1.785 (subtract them)
4x + 2z = 1.14
-----------------
3x = 0.645
x = 0.215
------------
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!
abbey yaar, Adi tera Answer wrong hai, the answer comes close to 0.31 . and think about this, because the area of the red outlined section was 0.57, and your answer(area of z, which is the largest portion of the red outlined part) is not even 1/3 of that area(0.57). I did this with my own method and got answer as 0.31 unit squared.
Post by: nid404 on October 16, 2009, 07:27:38 am
sameer put down ur method,,,i can ask mam if it is right or not
Post by: sameer210394 on October 16, 2009, 07:54:54 am
refer to the diagram attached..
.
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)
----------------------------------
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
--
now for the final sim. equations
7x + 2z = 1.785
2x + z = 0.57 (*2)
--------------------
7x + 2z = 1.785 (subtract them)
4x + 2z = 1.14
-----------------
3x = 0.645
x = 0.215
------------
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.
Post by: nid404 on October 16, 2009, 07:59:48 am
Post by: sameer210394 on October 16, 2009, 08:05:09 am
okay sameer when she first gave us the question, she gave us the hint that we needed to use the semi circle thing. But I can show this to her....It's too long a thing and she said it is not a very long thing.....No.1 she approved of our answer.....maybe in a haste she might have....cuz i asked her during the library hours. I will ask her again
only the explanation is lengthy, if you solve it in a paper, it is less than 4 steps... try 4 ur self..
and plzz ask your teacher...
Post by: nid404 on October 16, 2009, 08:25:17 am
Post by: astarmathsandphysics on October 16, 2009, 09:03:12 am
Post by: Ghost Of Highbury on October 16, 2009, 09:04:11 am
I found a mistake. I am trying to do it now.
yeah..the substituting part..noticed it rite now..
Post by: astarmathsandphysics on October 16, 2009, 10:20:46 am
Post by: Ghost Of Highbury on October 16, 2009, 10:24:19 am
Try this
ohh..sry..my bad..tks sameer..
Post by: nid404 on October 16, 2009, 10:24:31 am