The area of a sector of a circle is ½ r² ∅, where r is the radius and ∅ the angle in radians subtended by the arc at the centre of the circle. So in the below diagram, the shaded area is equal to ½ r² ∅ . We also have that
[tex]180\text{ grados = }\pi\text{ rad }[/tex]For thus we have that the angle 260 in radians is
[tex]260\cdot\frac{\pi\text{ rad}}{180}=1.444\text{ }\pi\text{ rad}[/tex]So the area of that sector is
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(4)^2\cdot(1.444\text{ }\pi\text{ rad)} \\ =\frac{16}{2}\cdot(1.444\text{ }\pi\text{ rad)} \\ =\text{ 8 }\cdot(1.444\text{ }\pi\text{ rad)} \\ =\text{ 11.5555 }\pi\text{ rad} \end{gathered}[/tex]The answer is 11.5555 pi rad.