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

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

60

step-by-step explanation: