The formula is ,
[tex]\begin{gathered} =\pi r^2 \\ =\frac{\theta}{360}\times\pi\times r^2 \end{gathered}[/tex]If the area of the given quater of the circle is given then we can find the value of theta.
And if the arc length is given then we can also find the angle
[tex]\begin{gathered} l=\theta\times r \\ \theta=\frac{l}{r} \end{gathered}[/tex]