Calculate the area - really stuck The circle is given by $x^2+y^2=25$.
FGHI are midpoints on the rhombus
Calculate the area of FGLMHIJK (taking into account the curved lines)

 A: No calculus needed here.  We need to deduct the area of the four circular segments.  We have $r=5$.  To get the coordinates of $L$, we have $x^2+y^2=25; y=\frac 43(6-x)$, which gives $(x,y)=(\frac {117}{44},\frac {25}{44})$.  Now compute $c=\sqrt{(\frac {117}{44}-3)^2+(4-\frac {25}{44})^2}=\frac {\sqrt{14930}}{44}$ and get the area.
A: My first instinct would be to take these steps:


*

*Compute the radius of the circle using $G$. (Oh, you were given the radius. I didn't even see that until just a moment ago.)

*Use the radius to find $L$'s location.

*Write an equation for the circle and the rhombus side in the first quadrant, and then use integral calculus to find out the area of the sliver between $G$ and $L$.

*Then, I would compute the area of the circle sector in the first quadrant, then subtract the sliver area from the last bullet point.

*Finally, I would appeal to symmetry and multiply by 4.

A: draw $EG=5$ , $EL=5$ and $EH \bot GL$. first note that $EH=(6.8)/10=4.8$ by the area.
in $EGH$ using pyth. theo. $GH=7/5$.  $\tan (GEH)=7/24$ so $\tan(GEL)=\tan(2.(GEH))$ now you can find  $\angle GEL$. finding area between arc and trinagle is easy. 
