Answer:
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
