Answer:
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
