SOLUTION: what is the perimeter of a regular dodecagon (a polygon which has 12 sides)whose area is 24 + 12 sqrt(3).

Question 568980: what is the perimeter of a regular dodecagon (a polygon which has 12 sides)whose area is 24 + 12 sqrt(3).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
To calculate the area of regular polygon with N sides, the polygon can be sliced pizza-style into N isosceles triangles with one side as the base, and the area of those triangles can be calculated.
The height of those triangles is called the apothem, and can be calculated based on the length of the side, s, and half of the vertex angle, which depends on the number of sides, N.
For a dodecagon, the half of the vertex angle is
Putting it all together, the area, , of a regular polygon with sides of length is
or if you prefer your angles in degrees.
With , --> -->
as can be calculated from and using the formula (trigonometric identity) for tangent of a difference.
So with and gives us

The length of a side of the polygon is
and the perimeter is
RELATED QUESTIONS
A dodecagon is a polygon with 12 sides. How many degrees is each of the interior angles... (answered by jim_thompson5910)

A regular polygon has an interior angle that measures 144 degrees, and a side of which... (answered by Earlsdon,richwmiller)

What is the area of a regular hexagon whose radius is 24? I have that the apothem is 12... (answered by Alan3354)

Find the measrue of an angle in each polygon if the polygon is regular. Round to the... (answered by Alan3354)

A Canadian nickel has the shape of a regular dodecagon (12 sides). How many degrees are... (answered by ikleyn)

a regular polygon has 12 sides... what is the measurements of each interiot angle?... (answered by stanbon)

Find the perimeter in inches of a regular polygon whose area is 24 square root 3 inches,... (answered by ikleyn)

How many diagonals does a 12-sided regular polygon have? A regular polygon has sides of... (answered by scott8148)

Each exterior angle of a regular polygon is 12 how many sides does the polygon... (answered by Alan3354)