A regular polygon is inscribed in a circle of radius 9 cm. Calculate the perimeter of the polygon to the nearest tenth if the polygon has 6 sides.
recall that a regular hexagon has sides equal to the circle's radius.
To calculate the perimeter of the regular polygon, we need to find the length of one side.
The formula to find the length of one side of a regular polygon inscribed in a circle is:
Side length = 2 * radius * sin(π/number of sides)
In this case, the radius of the circle is 9 cm, and the number of sides is 6.
Substituting these values into the formula:
Side length = 2 * 9 cm * sin(π/6)
Using the approximation of π as 3.14:
Side length = 2 * 9 cm * sin(3.14/6)
Side length = 18 cm * sin(0.5236)
Now, use a calculator to find the sine of 0.5236:
sin(0.5236) ≈ 0.5
Substituting this value back into the equation:
Side length ≈ 18 cm * 0.5
Side length ≈ 9 cm
Since the regular polygon has 6 sides, the perimeter is given by:
Perimeter = 6 * side length
Perimeter ≈ 6 * 9 cm
Perimeter ≈ 54 cm
Therefore, the perimeter of the polygon is approximately 54 cm.
To calculate the perimeter of a regular polygon, you need to know the length of one side. In this case, we can find the length of one side by dividing the circumference of the circle by the number of sides.
1. Calculate the circumference of the circle:
Circumference = 2 * π * radius
Given that the radius is 9 cm, we have:
Circumference = 2 * 3.14 * 9
= 56.52 cm
2. Calculate the length of one side:
Length of one side = Circumference / Number of sides
Given that the polygon has 6 sides, we have:
Length of one side = 56.52 cm / 6
= 9.42 cm
3. Calculate the perimeter of the polygon:
Perimeter = Length of one side * Number of sides
Given that the polygon has 6 sides and the length of one side is 9.42 cm, we have:
Perimeter = 9.42 cm * 6
= 56.52 cm
Therefore, the perimeter of the polygon, to the nearest tenth, is 56.5 cm.