It is given that the sector made an angle of 90 degree at the centre and radius of circle is 13 cm.
Now if a sector makes an angle 'y' at the centre of a circle of radius 'r' then its area is given by:-
[tex]A=\frac{y}{360}\times\pi\times r^2[/tex]
Now for the given circle we have y=90 and r=13.
So the area of the sector will be:
[tex]\begin{gathered} A=\frac{90}{360}\times\pi\times(13)^2 \\ =\frac{1}{4}\times\frac{22}{7}\times169 \\ =\frac{11\times169}{14} \\ =132.78 \\ =132.8 \end{gathered}[/tex]
So the area of sector is 132.8 cm. square.
