The following regular polygon has 15 sides. This distance from its center to any given vertex is 12 inches.

Which of the following is the best approximation for its perimeter?

Step-by-step explanation:

The distance from the center of a regular polygon to any given vertex is called the radius. For the given polygon, radius = 12 inches

The number of sides that the polygon has is 15 sides.

The perimeter of a polygon is the distance around it. We would find the length of each side by applying the formula,

radius = s/[2 sin  (180/n) ]

where

s is the length of any side

n is the number of sides

Therefore,

12 = s/[2Sin (180/15) ]

12 = s/2Sin12

s = 12 * 2Sin12

s = 4.98988056

Perimeter = number of sides * length of each side

Perimeter = 4.98988056 * 15 = 74.84 inches

75 inches

Step-by-step explanation:

Step-by-step explanation:

The distance from the center of a regular polygon to any given vertex is called the radius. For the given polygon, radius = 12 inches

The number of sides that the polygon has is 15 sides.

The perimeter of a polygon is the distance around it. We would find the length of each side by applying the formula,

radius = s/[2 sin  (180/n) ]

where

s is the length of any side

n is the number of sides

Therefore,

12 = s/[2Sin (180/15) ]

12 = s/2Sin12

s = 12 * 2Sin12

s = 4.98988056

Perimeter = number of sides * length of each side

Perimeter = 4.98988056 * 15 = 74.84 inches

Finally round your answer and its 75 inches