MathDB
2018 Individual #12

Source:

January 13, 2023
2018 Individual

Problem Statement

A unit cube is sliced by a plane passing through two of its vertices and the midpoints of the edges it passes through. What is the area of the rhombus formed by this intersection?
https://cdn.artofproblemsolving.com/attachments/3/5/3ed19fa0b4d454a3afc16c6bcf9d69403f6b2c.png
<spanclass=latexbold>(A)</span>62<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>6<spanclass=latexbold>(E)</span>26<span class='latex-bold'>(A) </span> \dfrac{\sqrt6}{2}\qquad<span class='latex-bold'>(B) </span>\sqrt2\qquad<span class='latex-bold'>(C) </span>\sqrt3\qquad<span class='latex-bold'>(D) </span>\sqrt6\qquad<span class='latex-bold'>(E) </span>2\sqrt6