2021 Fall AMC 12A Problems/Problem 14
Revision as of 19:04, 23 November 2021 by Ehuang0531 (talk | contribs) (→Solution (Law of Cosines and Equilateral Triangle Area))
Solution (Law of Cosines and Equilateral Triangle Area)
Isosceles triangles ,
, and
are identical by SAS similarity.
by CPCTC, and triangle
is equilateral.
Let the side length of the hexagon be . The area of each equilateral triangle is
. By the Law of Cosines, the square of the side length of equilateral triangle BDF is
. Hence, the area of the triangle is
. So the total area of the hexagon is
and
.