the equation of the line joining (-4,-3) and (0,5) is
(y+3)/(x+4)=2
2x-y+5=0
sub y=0, x=-5/2
the equation of the line joining (-4,-3) and (5,0) is
(y+3)/(x+4)=1/3
x-3y-5=0
sub x=0, y=-5/3
so
the area of the shaded region
=(5+5/3)(4)/2+1/4*pi*5^2+5*(5/3)/2
=37.1350