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7
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Part of
2018 Stanford Mathematics Tournament
Problems
(1)
SMT 2018 Geometry #7 3d
Source:
8/8/2023
Two equilateral triangles
A
B
C
ABC
A
BC
and
D
E
F
DEF
D
EF
, each with side length
1
1
1
, are drawn in
2
2
2
parallel planes such that when one plane is projected onto the other, the vertices of the triangles form a regular hexagon
A
F
B
D
C
E
AF BDCE
A
FB
D
CE
. Line segments
A
E
AE
A
E
,
A
F
AF
A
F
,
B
F
BF
BF
,
B
D
BD
B
D
,
C
D
,
CD,
C
D
,
and
C
E
CE
CE
are drawn, and suppose that each of these segments also has length
1
1
1
. Compute the volume of the resulting solid that is formed.
geometry
3D geometry