Answer:
Area = 259.8 cm²
Step-by-step explanation:
Central Angle = 360/6 = 60 degrees
The half of which is 30 degrees
So,
=> Tan 30 = [tex]\frac{opposite}{adjacent}[/tex] (Considering it a right angled triangle)
Where opposite = 1/2 s and adjacent = 5√3 cm
=> 0.577 * 5√3 = 1/2 s
=> 1/2 s = 5
So,
=> s = 10 cm
Perimeter = 6s = 6(10) = 60 cm
Area of Regular Polygon = [tex]\frac{1}{2} (Apothem)(Perimeter)[/tex]
Area = [tex]\frac{1}{2} (5\sqrt{3} )(60)[/tex]
Area = (5√3)(30)
Area = 259.8 cm²
