2017 COMC B3
Source:
October 12, 2018
Comc2017 COMC
Problem Statement
Source: 2017 Canadian Open Math Challenge, Problem B3
—--
Regular decagon (10-sided polygon) has area square units. Determine
the area (in square units) of the rectangle .[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,NE);
label("",B,NE);
label("",C,NW);
label("",D,NW);
label("",E,E);
label("",F,E);
label("",G,SW);
label("",H,S);
label("",I,SE);
label("",J,2*dir(0));
fill(C--D--H--I--cycle,mediumgrey);
draw(polygon(10));
[/asy]