Find the area of the shaded region .

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