The answer is a. a circle is inscribed in a regular hexagon with side length 10 feet. what is the area of the shaded region? recall that in a 30 – 60 – 90 triangle, if the shortest leg measures x units, then the longer leg measures x√3 units and the hypotenuse measures 2x units.(150√3 - 75π) ft^2(300 – 75π) ft^2(150√3 – 25π) ft^2(300 – 25π) ft^2

Option A. (150√3- 75π) ft².

Step-by-step explanation:

In the given picture a circle is inscribed in a regular hexagon with a side length = 10 feet.

Formula of the area of a regular hexagon

                                                              =

                                                             = 3√3×50 = 150×√3 feet²

Now we will calculate the area of circle inscribed.

Already given in the question that In a 30-60-90 triangle

Longer leg of triangle r = x√3 = = 5√3 feet

Now area of circle = π r² = π(5√3)² = 75π feet²

Area of shaded part = Area of Hexagon-Area of circle inscribed.

                                 = (150√3 - 75π) ft²