Answer:
- C. 150√3
Step-by-step explanation:
Radius of the inscribed circle is the apothem of the hexagon.
Apothem (a) and half of the side (s) make a 30-60-90 right triangle.
<u>The ratio of the legs, as per property of 30-60-90 triangle:</u>
- s : a = 1 : √3 ⇒ s : 5√3 = 1 : √3 ⇒ s = 5
Half the side is s = 5 units, then side of the hexagon is 10 units.
<u>The area of the hexagon:</u>
- A = 1/2Pa, P- perimeter, a- apothem
- A = 1/2(6*10)*(5√3) = 150√3
Correct choice is C
