#### Answer

68.4 in

#### Work Step by Step

Given in a regular polygon,each central angle measures 30$^{\circ}$
Each side of the polygon =5.7 in
We need to find the perimeter of the polygon
We know the relationship between the central angle and number of sides
Central angle = $\frac{360 ^{\circ} }{n}$
30 $^{\circ}$ = $\frac{360 ^{\circ} }{n}$
n = $\frac{360}{30}$ = 12
Therefore the polygon consist of 12 sides
The perimeter of polygon = np
= 12*5.7
= 68.4 in