(a) sin x° = 0.8
1 answer:
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Answer:
Area of the shaded region = 3.46 square units
Step-by-step 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
