Answer:
Area of the shaded region = 3.46 square units
Explanation:
Measure of the interior angle of a regular polygon =

From the picture attached,
Number of sides of the given polygon 'n' = 6
Interior angle (∠BAF) of the given polygon =

= 120°
Measure of ∠BAC =

= 30°
Now we apply sine rule in ΔAGB,
sin(30°) =

=

BG = AB[sin(30°)]
=

= 1
By applying cosine rule in ΔABG,
cos(30°) =

=

AG = AB[cos(30°)]
=

=

AC = 2(AG)
= 2√3
Area of ΔABC =

=

=

=

Area of the shaded region = Area of ΔABC + Area of ΔFED
= 2(Area of ΔABC)
= 2√3
= 3.46 square units