Answer:
Area of the region = 15.03 in²
Step-by-step explanation:
Area of region between a regular hexagon with sides 6" and circle inscribed.
So Area of region = Area of regular hexagon - area of circle
Now area of regular hexagon = [tex]\frac{3a^{2} \sqrt{3}}{2}[/tex]
where a = side of the hexagon = 6"
Now area of regular hexagon = [tex]\frac{3(6^{2})\sqrt{3}}{2}=\frac{108\sqrt{3}}{2}[/tex] = 93.53 square in.
Area of circle inscribed = πr²
Here r is the radius of the circle = [tex]\sqrt{6^{2}-3^{2}}=\sqrt{36-9}[/tex]
r = 5"
So area of the inscribed circle = π(5)² = 3.14(25) = 78.5 square in.
Now area of region = 93.53 - 78.5 = 15.03 in²
