Answer
$Area = \oint_{C} x \ dy $
and
$Area = - \oint_{C} y \ dx $
Work Step by Step
The tangential form for Green Theorem is given as:
$Area = \iint_{R} \ dx \ dy = \iint_{R} 1+0 \ dx \ dy$
or, $Area = \iint_{R} (\dfrac{\partial x}{\partial x}-\dfrac{\partial (0)}{\partial y}) dx dy =\oint_{C} x \ dy $
Similarly, $Area=\iint_{R} 0+1 \ dx \ dy$
or, $Area = \iint_{R} (\dfrac{\partial (0)}{\partial x}-\dfrac{\partial (y)}{\partial y}) dx dy =- \oint_{C} y \ dx $
