What is the area of a regular hexagon with a radius of 7square root 3?

Question

What is the area of a regular hexagon with a radius of 7square root 3?

Answer 1

A = 1/2ap, where a is the apothem (radius) and p is the perimeter

The apothem of a regular hexagon is always 1/2s*sqrt3, where s is one of the side lengths, so a side length of this hexagon is 14. Thus the perimeter of the hexagon is 14*6 = 84.

A = 1/2ap

1/2(7sqrt3)(84)

42(7sqrt3)

294sqrt3 square units <===ANSWER

Answer 2

What is the area of a regular hexagon with a radius of 7square root 3?

cece_121...here it is:

http://www.flickr.com/photos/27678773@N0...

In the Hexagon the central angle = 60°

Hexagon has 6 sides

360° ÷ 6 = 60°

The Area of the sector with central Angle = 60°

From the Diagram

Cos 60° =  AC/AO

AC = AO  Cos 60°

AC = 7√3 (0.5)

Area Equilateral Triangle = ½ Base x Height

Area Equilateral Triangle = ½ AC x OC

Sin 60° = OC /OA

OC =  OA Sin 60°

OC =  7√3 (0.866)

Area Equilateral Triangle = ½ AC x OC

Area Equilateral Triangle = ½ (7√3 )( 0. 5) x 7√3 (0.866)

Area Equilateral Triangle =  (7√3 x 7√3 (0.866)(0.25)

Area Equilateral Triangle = 49(3) x (0.866) (0.25)

Area Equilateral Triangle =  31. 83

Area of the Hexagon = Area of the Triangle x  6

Area of the Hexagon = 31. 83  x  6

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Ans::Area of the Hexagon = 190. 95

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Hope this helps