Required area $=4 \times area $ in the first quadrant
$A=\int \limits_0^{ae} \; y dx $
$\qquad=\bigg[(e= \sqrt {1-\large\frac{b^2}{a^2}})\bigg]$
$\qquad=4 \int \limits_0^2 \sqrt {1-\large\frac{x^2}{9}}$$dx$
$\qquad=4 \large\frac{\sqrt 5}{3} $$\int \limits _0^2 \sqrt {3^2 -x^2}dx$
$\qquad=4 \large\frac{\sqrt 5}{3} $$ \bigg[\large\frac{3^2} {2} $$\sin ^{-1} \large\frac{x}{3}+\frac{x}{2} $$\sqrt {3^2-x^2}\bigg]_0^2$
$\qquad=4 \large\frac{\sqrt 5}{3} $$ \bigg[\large\frac{9} {2} $$\sin ^{-1} \large\frac{2}{3}$$+\sqrt 5\bigg]$sq.units