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Find the Area of abcd

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Find the area of the region ABCDABCD.

geometry circle

In the Figure □PQRS◻PQRS is a square with side 26–√26.

By joining the midpoints another square □WXYZ◻WXYZ is formed .

Circles are drawn with 44 vertices as the center and

radius equal to the side of the square □WXYZ◻WXYZ.

Find the area common to all the 44 circles .

a.)6π(3–√−12)b.)4π−33–√c.)12(π−33–√)d.)4π−12(3–√−1)✓a.)6π(3−12)b.)4π−33c.)12(π−33)d.)4π−12(3−1)✓

So i have to find the area of region ABCDABCD.

I have found that WX=WY=YZ=XZ=23–√.WX=WY=YZ=XZ=23.

Let Region WBAWBA=Region XADXAD=Region ZCDZCD=Region YBC=aYBC=a

and

Region WAXWAX=Region XDZXDZ=Region ZCYZCY=Region YBW=bYBW=b

and

Region ABCD=mABCD=m

Area(□WXYZ)=12m+4a+4b=12Area(◻WXYZ)=12m+4a+4b=12.

Area of sectors.

AreaArea(sector WZYWZY)=AreaArea(sector XYZXYZ)=AreaArea(sector WXYWXY)=AreaArea(sector WZXWZX)=m+3a+2b=3πm+3a+2b=3π.

Now i m stucked.

I m looking for simple short way.

I have studied maths upto 12th12th grade.