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2017 Canadian Open Math Challenge
B3
B3
Part of
2017 Canadian Open Math Challenge
Problems
(1)
2017 COMC B3
Source:
10/12/2018
Source: 2017 Canadian Open Math Challenge, Problem B3 —-- Regular decagon (10-sided polygon)
A
B
C
D
E
F
G
H
I
J
ABCDEFGHIJ
A
BC
D
EFG
H
I
J
has area
2017
2017
2017
square units. Determine the area (in square units) of the rectangle
C
D
H
I
CDHI
C
DH
I
.[asy] pair A,B,C,D,E,F,G,H,I,J; A = (0.809016994375, 0.587785252292); B = (0.309016994375, 0.951056516295); C = (-0.309016994375, 0.951056516295); D = (-0.809016994375, 0.587785252292); E = (-1, 0); F = (-0.809016994375, -0.587785252292); G = (-0.309016994375, -0.951056516295); H = (0.309016994375, -0.951056516295); I = (0.809016994375, -0.587785252292); J = (1, 0); label("
A
A
A
",A,NE); label("
B
B
B
",B,NE); label("
C
C
C
",C,NW); label("
D
D
D
",D,NW); label("
E
E
E
",E,E); label("
F
F
F
",F,E); label("
G
G
G
",G,SW); label("
H
H
H
",H,S); label("
I
I
I
",I,SE); label("
J
J
J
",J,2*dir(0)); fill(C--D--H--I--cycle,mediumgrey); draw(polygon(10)); [/asy]
Comc
2017 COMC