As we are not told if the beams are straight or not, then by having the perfect curvature to form a perfect circle we will have the maximum area. The circumference would be (12×16=) 192 feet (using circumeference = 2 x (pi) x radius).
This would give a radius of 30.5578 feet.
The area (pi x r-squared) would be 2,933.55 feet squared.
______________
(If the beams are straight then the maximum area is a regular dodecagon of side 16 feet. This area would be 2,866.21 feet sq.)

Well i don’t really know what a beam is becouse i am not english or american but if we have a dozen of them (12) and each one is 16 feet and as you say they are straight things…we can make a square with a side of a = 3 beams = 3 *16 = 48 foot. to calculate the land it includes we multiply 48 * 48 = 2304…but this doesn’t match with the other answers…what am i missing?

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joe| Profile April 12th, 2010 - 8:31 amAs we are not told if the beams are straight or not, then by having the perfect curvature to form a perfect circle we will have the maximum area. The circumference would be (12×16=) 192 feet (using circumeference = 2 x (pi) x radius).

This would give a radius of 30.5578 feet.

The area (pi x r-squared) would be 2,933.55 feet squared.

______________

(If the beams are straight then the maximum area is a regular dodecagon of side 16 feet. This area would be 2,866.21 feet sq.)

Shawn| PUZZLE GRANDMASTER | Profile April 12th, 2010 - 11:00 am2,866.215 ft^2, if arranged into a 12-sided figure

Hex| PUZZLE MASTER | Profile April 12th, 2010 - 1:51 pmI guess a 12 sided polygon should yield the biggest area.

A = 12 x L x D / 2

tan alpha = L / 2 / d

A = 3 x L^2 / tan(360/24) = 2,866.22 sq ft

Falwan| Profile April 12th, 2010 - 11:38 pmArea of a dodecagon (12 sided ) = 11.19615242 * a * a = 11.19615242 (16)(16) = 2866.21501952 sq. ft.

Bobo The Bear| PUZZLE MASTER | Profile April 13th, 2010 - 2:24 pmThe greatest area would be enclosed by a regular dodecagon.

The area would be 2866.215 square feet.

brianu| Profile April 13th, 2010 - 7:33 pm2967.32 square feet

cheddarmelt| Profile April 14th, 2010 - 9:01 pmfor regular polygons, area = {(S^2)N}/{4 tan (pi/N)}, where S=side length and N=number of sides, and tangent is in radians.

I came up with 2866 sq ft.

Hendy| Profile April 17th, 2010 - 11:42 amFirst cheat and go to http://en.wikipedia.org/wiki/Dodecagon.

Second enter the side length.

Third do the calculations.

Four post the answer. A = 2866.2150202129

ihavenoorgans| Profile September 21st, 2010 - 1:04 pmUse three beams to make a triangle around yourself and declare yourself to be on the outside. You have now enclosed the entire planet.

Tsopi| Profile October 18th, 2010 - 2:06 pmWell i don’t really know what a beam is becouse i am not english or american but if we have a dozen of them (12) and each one is 16 feet and as you say they are straight things…we can make a square with a side of a = 3 beams = 3 *16 = 48 foot. to calculate the land it includes we multiply 48 * 48 = 2304…but this doesn’t match with the other answers…what am i missing?