Find the area of the regular hexagon if the radius of a circle inscribed in the hexagon is 10√3
1 answer:
Answer:
- D. 600√3
Step-by-step explanation:
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<u>Refer to your previous question: </u>
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 : 10√3 = 1 : √3 ⇒ s = 10
Half the side is s = 10 units, then side of the hexagon is 20 units.
<u>The area of the hexagon:</u>
- A = 1/2Pa, P- perimeter, a- apothem
- A = 1/2(6*20)*(10√3) = 600√3
Correct choice is D
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