MathDB

Polyhedron

Source: AIME 2002 #15

November 28, 2005

geometrytrapezoidanalytic geometryvector

Problem Statement

Polyhedron

ABCDEFG

has six faces. Face

ABCD

is a square with

AB=12;

face

ABFG

is a trapezoid with

\overline{AB}

parallel to

\overline{GF},

BF=AG=8,

and

GF=6;

and face

CDE

has

CE=DE=14.

The other three faces are

ADEG, BCEF,

and

EFG.

The distance from

E

to face

ABCD

is 12. Given that

EG^2=p-q\sqrt{r},

where

p, q,

and

r

are positive integers and

r

is not divisible by the square of any prime, find

p+q+r.

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