Question #a4633

1 Answer
CW
May 24, 2017

#54sqrt3 " cm"^2#

Explanation:

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A regular hexagon can be divided into 6 congruent equilateral triangles. As shown in the figure, #DeltaOAB# is one of the 6 congruent equilateral triangles.
#=> OA=OB=AB=6 cm#
Area of an equilateral triangle #A_e=sqrt3/4a^2#,
where #a# is the length of the side of the triangle.
#=> A_e=sqrt3/4*6^2=sqrt3/4*36=9sqrt3 " cm"^2#

Hence, Area of hexagon #A_h=6*A_e=6*9sqrt3=54sqrt3 " cm"^2#

Alternatively, you can use the following formula to determine #A_h# when the side #(a)# of a regular hexagon is given:

#A_h=(3sqrt3)/2*a^2=(3sqrt3)/2*6^2=(3sqrt3)/2*36=54sqrt3 " cm"^2#

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