Find the area of the polygon

Step-by-step explanation:

Assuming a perpendicular line(apotherm) is extended from the midpoint of the polygon to the midpoint of one of its sides, then we can determine the length of the apotherm by applying Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Let a represent the apotherm

Hypotenuse = 4

Apotherm = a

Opposite = a(apotherm = length of each side/2)

Therefore,

4² = a² + a²

16 = 2a²

a² = 16/2 = 8

a = √8 = 2√2

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

Area = a² × n × tan 180/n

Where n represents the number of sides of the polygon.

n = 6

Therefore,

Area = (2√2)² × 6 × tan(180/6)

Area = 48 × tan 30

Area = 27.2

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.