Find the area of the region between a regular hexagon with sides of 6" and its inscribed circle.

  (54√3 - 27π) in²

Step-by-step explanation:

The radius of the inscribed circle is the apothem of the hexagon, so is ...

  (6 in)·sin(60°) = 3√3 in

The area of the hexagon is half the product of this and the perimeter of the hexagon (6 times the side length).

  A = (1/2)(6·6 in)(3√3 in) = 54√3 in²

The area of the circle is ...

  A = π·r² = π(3√3 in)² = 27π in²

Then the region between the hexagon and its inscribed circle will be ...

  hexagon area - circle area =

  (54√3 - 27π) in²

seems like d

step-by-step explanation: