We know that, Area of a Circle is given by : πR²
Where : R is the Radius of the Circle.
We can Notice that : The Given Figure is One - Fourth of the Circle with Radius 'R'
[tex]\mathsf{\implies Area\;of\;One\;Quarter\;of\;the\;Circle = \frac{\pi R^2}{4}}[/tex]
We can Notice that : The Quarter of the Circle is divided into 3 Equal Parts and The Shaded Region is One of the Equal Part.
[tex]\mathsf{\implies Area\;of\;Shaded\;Region = \frac{\frac{\pi R^2}{4}}{3}}[/tex]
[tex]\mathsf{\implies Area\;of\;Shaded\;Region = {\frac{\pi R^2}{12}}}[/tex]
