7. In a regular n-gon, the sides are 4.8 cm in length, the apothem is 7.4 cm, and the area is

177.6 cm2

How many sides are in the polygon?

sides

Answer: the polygon has 10 sides.

Step-by-step 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