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)


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.
