MathDB

2014 Geometry #9

Source:

July 12, 2022

2014Geometry Test

Problem Statement

We have squares

ABCD

and

EFGH

. Square

ABCD

has points with coordinates

A=(1,1,-1)

,

B=(1,-1,-1)

,

C=(-1,-1,-1)

and

D=(-1,1,-1)

. Square

EFGH

has points with coordinates

E=(\sqrt{2},0,1)

,

F=(0,-\sqrt{2},1)

,

G=(-\sqrt{2},0,1)

, and

H=(0,\sqrt{2},1)

. Consider the solid formed by joining point

A

to

H

and

E

, point

B

to

E

and

F

, point

C

to

F

and

G

, and point

D

to

G

and

H

. Compute the volume of this solid.

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