Problem:
A cube with side length is sliced by a plane that passes through two diagonally opposite vertices and and the midpoints and of two opposite edges not containing or , as shown. What is the area of quadrilateral ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
All sides of are of equal length, so is a rhombus. Its diagonals have lengths and , so its area is
The problems on this page are the property of the MAA's American Mathematics Competitions