Answer: the polygon has 10 sides.
Explanation:
The formula for determining the area of a regular polygon is expressed as
Area = pa/2
Where
P represents the perimeter of the polygon.
a represents the apotherm of the polygon. The apotherm is the perpendicular distance from the center of one side of the polygon to the center of the polygon.
n represents the number of sides that the polygon has.
From the information given, the
Perimeter = n × 4.8 = 4.8n
Area of polygon = 177.6 cm²
apotherm = 7.4 cm
Therefore,
177.6 = (4.8n × 7.4)/2
Cross multiplying by 2, it becomes
177.6 × 2 = 35.52n
355.2 = 35.52n
n = 355.2/35.52
n = 10