To find the perimeter of a regular hexagon, you can use the formula: Perimeter = 6 × Length of one side.
Given that the apothem (distance from the center to a side, forming a right angle) is 9, we can find the length of one side using trigonometry.
In a regular hexagon, the apothem (a) and the side length (s) are related by:
a = (s/2) × √3
So, we can solve for the side length:
s = 2 × a / √3
s = 2 × 9 / √3
s = (18 / √3)
To rationalize the denominator:
s = (18 × √3) / 3
s = 6√3
Now, we can find the perimeter:
Perimeter = 6 × 6√3
Perimeter = 36√3
So, the perimeter of the regular hexagon with an apothem of 9 is 36√3.
Answer:
163 times the square root of 3
Step-by-step explanation:
The apothem is the length from the center of a regular polygon to the midpoint of one of its sides. It is perpendicular (90∘) to the side.
