find the base of the triangle:
sin130/b=sin((180-130)/2)/15.4
b=15.4sin130/sin25
Now find the height...
sin90/15.4=sin25/h
h=15.4sin25/sin90
Now we can find the area of the triangle with the h and b found above...
A=bh/2=90.83755
Now we find the area of the circle:
A=(apr^2)/360
A=130p(15.4^2)/360=269.0494855
And finally you subtract the triangle's area from the area of that 130° sector of the circle...
A=178.2119355 and since we only have 3 significant figures for the radius...
A=178 cm^2
