By the Pythagorean Theorem, the hypotenuse of the right triangle is 

 inches.

The sidelength of the octagon is therefore 

 inches,

and the perimeter of the regular octagon, which has eight sides of equal length, is 

 inches, 

or 

 feet.

The answer is independent of the sidelength, so we can assume without loss of generality that the sidelength is 1. The equilateral triangle, the square, the pentagon, the hexagon, and the octagon have 3, 4, 5, 6, and 8 sides of equal length, respectively, so their perimeters are 3, 4, 5, 6, and 8. 

The median of these perimeters is the middle perimeter, 5. The midrange of these perimeters is the mean of the greatest and the least perimeters:

The midrange, (B), is greater.

The answer is independent of the sidelength, so we can assume without loss of generality that the sidelength is 1. The square, the pentagon, the hexagon, and the octagon have 4, 5, 6, and 8 sides of equal length, respectively, so their perimeters are 4, 5, 6, and 8. The mean of these four perimeters is

 units.

The median is the mean of the middle two perimeters, which are 5 and 6:

The mean, (A), is greater.

The figure referenced is below:

Pentagon  is regular, so all of its sides have the same length; we will examine  in particular. The perimeter of Pentagon  is the sum of the lengths of its sides, which is .

Since  is also a side of Square , it follows that ; since  is also a side of equilateral , . The perimeter of Pentagon  is equal to 

,

the same as that of Pentagon .

By the Pythagorean Theorem, the hypotenuse of the right triangle is 

 inches, making its perimeter

 inches.

A regular decagon has ten sides of equal length, so each side measures

 inches.

A regular octagon has eight sides of equal length. The perimeter of this octagon is one meter, which is equal to 1,000 millimeters; each side, therefore, has length

 millimeters

making the quantities equal.

A regular pentagon has five sides of equal length; since one side is 72 units long, its perimeter is 

.

80% of this is 

,

so this is the length of the hexagon, and, since all six sides are of equal length, one side measures 

(B) is greater.

The solution is independent of the actual lengths, so we assume the pentagon has sidelength 1. Its perimeter is therefore 5. Subsequently, the octagon's perimeter is twice this, or 10, and its sidelength is one-eighth of this, or

.

The ratio of the sidelength of the octagon to that of the pentagon is

 or 5 to 4.

A regular octagon has eight sides of equal length. The perimeter, which is the sum of the lengths of these sides, is one mile, which is equal to 5,280 feet. Therefore, the length of one side is

. This makes the length of a side less than 880 feet.

The sides of the rectangle, in total, are divided into 18 segments of equal measure, as indicated below:

The rectangle has a total perimeter of 360, so each segment - one side of a square - measures . Each square has area , so the shaded portion of the rectangle, which comprises seven squares, has area

.