hellohello123 -

**Finding Coordinates of A',B',C',D'**
Find the normal vector N of the plane ABCD using cross product:

Each line

has the same direction as N, so the parametric equations are

. These four lines intersect the plane

when their z-value is zero (by construction). Therefore set

to solve for

, and plugging

back into

gives you the other two coordinates of

. Repeat to find

.

**Finding the Area of A'B'C'D'**
The area of a parallelogram

, the magnitude of the cross product of two adjacent sides.

**Finding the Volume of the contained area**
The volume of the figure is simply the area of

times the "height"

. So, using the parametric equation technique described above,

, find the coordinates of

, use the length of

as your height, and multiply by

, where

is the length of the side of the top face of the cube.