The area of the shaded region is   option first is correct.
 option first is correct.
It is given that a circle is inscribed in a regular hexagon with sides of 10 feet.
It is required to find the shaded area (missing data is attached shown in the picture).
<h3>What is a circle?</h3>
It is defined as the combination of points that and every point has an equal distance from a fixed point ( called the center of a circle).
We have a hexagon with a side length of 10 feet.
We know the area of the hexagon is given by:
 where a is the side length.
  where a is the side length.
 ⇒
 ⇒  
 
We have the shortest length = x feet and from the figure:
2x = 10 
x = 5 feet
The radius of the circle r = longer leg 
 feet
 feet
The area of the circle a =  ⇒
  ⇒  
  
The area of the shaded region = A - a 

Thus, the area of the shaded region is  
Learn more about circle here:
brainly.com/question/11833983