2022 AMC 12B Problems/Problem 10
Contents
Problem
Regular hexagon has side length
. Let
be the midpoint of
, and let
be the midpoint of
. What is the perimeter of
?
Solution
Consider triangle .
and
.
because it is an interior angle of a regular hexagon.<ref group = "note">The sum of the internal angles of any polygon with
sides is given by
. Therefore, the sum of the internal angles of a hexagon is
, and each internal angle of a regular hexagon measures
.</ref> By the Law of Cosines, we have:
By SAS Congruence, triangles ,
,
, and
are congruent, and by CPCTC, quadrilateral
is a rhombus. Therefore, its perimeter is
.
Notes
<references group = "note" />
See Also
2022 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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All AMC 12 Problems and Solutions |
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