MathDB

Let

A

be a corner of a cube. Let

B

and

C

the midpoints of two edges in the positions shown on the figure below: http://i.imgur.com/tEODnV0.png The intersection of the cube and the plane containing

A,B,

and

C

is some polygon,

P

.
[*] How many sides does

P

have? Justify your answer. [*] Find the ratio of the area of

P

to the area of

\triangle{ABC}

and prove that your answer is correct.

Problem Statement