Maths

[nid404]

Check the diagram below

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

[Ghost Of Highbury]

kya question hai be?

ekdum jhakaas~~

..will try

[Ghost Of Highbury]

but what are the four things touching the verteices of the square?

are they a sector

[nid404]

I don't think u can call it a sector

wait i'll try and make the drawing better

[nid404]

here i think this will be much clear

oh the sides are of 1 unit....i think i mentioned it before

please help me answer it

[astarmathsandphysics]

Call the triangle staring from a corner x, a tiangle on a side z and the one in the middle y
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

[nid404]

I don't know the answer....post your method anyway

@astar-they r not triangles is what i am specifically told by the teacher.....

[astarmathsandphysics]

I am not using any properties of triangle So method should work.

[nid404]

okay then...
when you get back home, could you do it with the diagram please??

[Ghost Of Highbury]

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!

[Ghost Of Highbury]

is this an A/AS level question??

[nid404]

thanks.....

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

[Ghost Of Highbury]

ur welcome...

[Ghost Of Highbury]

u asked ur ma'am?

[nid404]

i will know only on monday