MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
CHMMC problems
2012 CHMMC Spring
9
9
Part of
2012 CHMMC Spring
Problems
(1)
2012 Spring Team #9
Source:
3/20/2022
Let
S
S
S
be a square of side length
1
1
1
, one of whose vertices is
A
A
A
. Let
S
+
S^+
S
+
be the square obtained by rotating S clockwise about
A
A
A
by
3
0
o
30^o
3
0
o
. Let
S
−
S^-
S
−
be the square obtained by rotating S counterclockwise about
A
A
A
by
3
0
o
30^o
3
0
o
. Compute the total area that is covered by exactly two of the squares
S
S
S
,
S
+
S^+
S
+
,
S
−
S^-
S
−
. Express your answer in the form
a
+
b
3
a + b\sqrt3
a
+
b
3
where
a
,
b
a, b
a
,
b
are rational numbers.
geometry