Answer:
Cross section is a rectangle.
Area of cross section = 16 sqrt(2) = 22.63 sq. units (to 2 decimals)
Step-by-step explanation:
Given a cube.
top face ABCD is parallel and congruent to bottom face EFGH ........(1)
justified by the properties of cubes
Sides AE and CH are perpendicular to faces ABCD and EFGH ..........(2)
justified by the properties of cubes
Diagonals AC and EH are congruent ......................(3)
justified by (1), congruent top and bottom faces
Consider cross-section ACHE
AC is congruent and parallel to EH (1) & (3)
EA & HC are perpendicular to AC (2)
Therefore the quadrilateral ACHE is a rectangle.
Length of diagonal AC = sqrt(4^2+4^2) = 4 sqrt(2) ..........pythagoras theorem
AE = CH = DG = 4 properties of cube, all sides equal
Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2) = 22.63 sq. units
