Area (in sq. units) of the region outside $\frac{|x|}{2}+\frac{|y|}{3}=1$ and inside the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ is

$3 (π-2)$ $3 (4-π)$ $6 (π-2)$ $6 (4-π)$

$6 (π-2)$

Let A be the required area. Then, A = Area of the ellipse - Area of rhombus ABA' B' $⇒A=π(2) (3)-\frac{1}{2}(AA' × BB')$ $⇒A=6π-\frac{1}{2}(4×6)=6π-12=6 (π-2)$