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

Step-by-step explanation:

The given polygon is a square. To determine the apotherm which is the perpendicular line from the midpoint of the square, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Let a represent the apotherm

Apotherm = length of each side of the square.

Therefore

8² = a² + a² = 2a²

64 = 2a²

a² = 64/2 = 32

a = √32

The formula for determining the area of a polygon is

Area of polygon is

area = a^2 × n ×tan 180/n

Where n is the number of sides

(n = 4)

Area = √32² × 4 × tan(180/4)

Area = 128 × 1

Area = 128

The formula for determining the perimeter of a regular polygon is

P = 2 × area/apotherm

Perimeter = 2 × 128/√32

Perimeter = 45.3

78.59 is the mean

step-by-step explanation: