Final answer:
The perimeter of a regular pentagon inscribed in a circle with a 7cm radius is approximately 41.138 cm. This is calculated by determining the length of one side using the sine function and then multiplying it by the number of sides.
Step-by-step explanation:
The question asks us to find the perimeter of a regular pentagon inscribed in a circumference (circle) with a radius of 7 cm. To find the perimeter of a regular pentagon, we need to calculate the length of one side and multiply it by 5, since all sides of a regular pentagon are equal.
Each side of the pentagon can be calculated by using the trigonometric properties of a pentagon. A regular pentagon has a central angle of 360º divided by the number of sides, which is 5, giving us 72º. Using the formula for the sine of the central angle, we can find the length of half of one side of the pentagon, which will be sine(72º/2) multiplied by the radius. The full length of one side is therefore the aforementioned product multiplied by 2. The approximate value of sine(36º) is 0.5878, thus:
Side Length ≈ 2 * 7cm * 0.5878 ≈ 8.2276 cm
Therefore, the perimeter P of the pentagon is:
P = 5 * 8.2276 cm ≈ 41.138 cm
So, the perimeter of the regular pentagon inscribed in a circumference with a 7cm radius is approximately 41.138 cm.