Question

Find the perimeter and area of the regular polygon. Round answers to the nearest tenth.

Answer 1

Answer: Perimeter = 72.67

Area = 363.3

Step-by-step explanation:

The given polygon is a pentagon. The apotherm is the perpendicular line from the midpoint of the Pentagon to the base of one of its sides.

The formula for determining the area of a regular polygon is expressed as

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 5

Apotherm = 10

Therefore,

Area = 10² × 5 × tan(180/5)

Area = 500 × tan 36

Area = 363.3

The formula for determining the perimeter of a regular polygon is

P = 2 × area/apotherm

Perimeter = 2 × 363.3/10

Perimeter = 72.67