Question

Find the area of the regular hexagon if the radius of a circle inscribed in the hexagon is 10√3
meters.

Answer 1

Answer:

• D. 600√3  

Step-by-step explanation:

Refer to your previous question:

• https://brainly.com/question/22624022

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.

The ratio of the legs, as per property of 30-60-90 triangle:

• s : a = 1 : √3 ⇒ s : 10√3 = 1 : √3 ⇒ s = 10

Half the side is s = 10 units, then side of the hexagon is 20 units.

The area of the hexagon:

• A = 1/2Pa, P- perimeter, a- apothem
• A = 1/2(6*20)*(10√3) = 600√3

Correct choice is D