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Adygea Teachers' Geometry Olympiad
2017 Adygea Teachers' Geometry Olympiad
4
4
Part of
2017 Adygea Teachers' Geometry Olympiad
Problems
(1)
volume of pentahedron (2017 Adygea Teachers' Geometry Olympiad p4 RU)
Source:
6/21/2020
A regular tetrahedron
S
A
B
C
SABC
S
A
BC
of volume
V
V
V
is given. The midpoints
D
D
D
and
E
E
E
are taken on
S
A
SA
S
A
and
S
B
SB
SB
respectively and the point
F
F
F
is taken on the edge
S
C
SC
SC
such that
S
F
:
F
C
=
1
:
3
SF: FC = 1: 3
SF
:
FC
=
1
:
3
. Find the volume of the pentahedron
F
D
E
A
B
C
FDEABC
F
D
E
A
BC
.
geometry
3D geometry
tetrahedron
Volume