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Vietnam Contests
Hanoi Open Mathematics Competition
2013 Hanoi Open Mathematics Competitions
8
8
Part of
2013 Hanoi Open Mathematics Competitions
Problems
(1)
equal areas inside a pentagon (2013 HOMC Junior Q8 Senior Q8)
Source:
7/18/2019
Let
A
B
C
D
E
ABCDE
A
BC
D
E
be a convex pentagon and area of
△
A
B
C
=
\vartriangle ABC =
△
A
BC
=
area of
△
B
C
D
=
\vartriangle BCD =
△
BC
D
=
area of
△
C
D
E
=
\vartriangle CDE=
△
C
D
E
=
area of
△
D
E
A
=
\vartriangle DEA =
△
D
E
A
=
area of
△
E
A
B
\vartriangle EAB
△
E
A
B
. Given that area of
△
A
B
C
D
E
=
2
\vartriangle ABCDE = 2
△
A
BC
D
E
=
2
. Evaluate the area of area of
△
A
B
C
\vartriangle ABC
△
A
BC
.
geometry
pentagon
areas