common area of two equal squares
Source: Dutch NMO 2003 p2
September 21, 2019
geometrysquarearea
Problem Statement
Two squares with side lie exactly on top of each other.
One square is rotated around a corner point through an angle of degrees relative to the other square.
Determine the area of the common piece of the two squares.[asy]
unitsize (2 cm);pair A, B, C, D, Bp, Cp, Dp, P;A = (0,0);
B = (-1,0);
C = (-1,1);
D = (0,1);
Bp = rotate(-30)*(B);
Cp = rotate(-30)*(C);
Dp = rotate(-30)*(D);
P = extension(C, D, Bp, Cp);fill(A--Bp--P--D--cycle, gray(0.8));
draw(A--B--C--D--cycle);
draw(A--Bp--Cp--Dp--cycle);label("", (-0.5,0.1), fontsize(10));
[/asy]