Question

Assume δxi, δzi << dx, dy that is δt is small. Approximate the area A'B'C'D' as (A'D') · (A'B'). Neglect non–linear terms such as δxi · δzi; and obtain continuity equation (conservation of mass) such that ∇ · V~ = 0, where V~ is the velocity field.

Basically question asks me to obtain conversation of mass equation in 2-dimensional cartesian coordinates ( (∂u/∂x) + (∂w/∂z) = 0 ) by proving the area of fluid particle ABCD equals to A'B'C'D'.
(initially fluid particle is assumed to be rectangle and area of the rectangle is length*height=dx*dz. After short time it becomes A'B'C'D' and its area should be equal to the initial area.)