A circle is inscribed in a regular hexagon with side length 10 feet. What is the area of the shaded region?

A circle is inscribed in a regular hexagon with side length 10 feet. An apothem and 2 raddi are drawn to form 2 triangles with angles 30, 60, and 90 degrees. The area between the circle and the hexagon is shaded.

Recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures xStartRoot 3 EndRoot units and the hypotenuse measures 2x units.

(150StartRoot 3 EndRoot – 75π) ft2
(300 – 75π) ft2
(150StartRoot 3 EndRoot – 25π) ft2
(300 – 25π) ft2