How to find the area of a cross section of a cube.

[rogermiranda]

I wish I could draw the problem but I cant's so I will try to explain it. I have a cube. The lenghts of the sides of the cube is 8. Inside the center of this cube there is a cross section in the shape of a sqaure. The four corners of this square are the midpoints of the sides of the cube. I have to find the area of this cross section. Can someone give me some advice on how to solve this problem? Also, I would like advice on how to find the area of any cross section inside a cube. Is there a standard approach or technique to finding the areas of cross sections of cubes. Thanks!

[aquiles]

Hi,
Let us think of a cube of butter and cut it, not straight down as a normal human being would, but for some mathematical reason across. We have two wedges.
We are here concerned with the area of the larger face of the wedge, are we not?

The dimensions of this face is 8 by the diagonal of the cube.

The diagonal of the cube acording to Pytagoras (a real friend) is
8 square plus 8 square = 64 + 64 = two 64's under the radical or 8 (square root of 2).

So the area of the face is 8 times 8 (square root of 2) that is 64 times 1.44 some!
(and I do not know how to draw this either.)