MathDB

Intersection of Plane and Pyramid

Source: AIME I 2007 #13

March 15, 2007

geometry3D geometrypyramidsymmetryratioPythagorean TheoremAMC

Problem Statement

A square pyramid with base

ABCD

and vertex

E

has eight edges of length 4. A plane passes through the midpoints of

\overline{AE}

\overline{BC}

, and

\overline{CD}

. The plane's intersection with the pyramid has an area that can be expressed as

\sqrt{p}

. Find

p