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Answer :
Based on the concrete of the Pentagon and the available information, the correct answer is option C. 36.3cm
What is the Pentagon?
Pentagon is a term that is used to describe a flat 2D shape that has five sides and five vertices. The word “pentagon” comes from the Greek word “pentagonos”, which means “five-angled."
In this case, to find the perimeter of the pentagon we need to know the length of one of its sides.
However, knowing that the apothem (distance from the center to any side) is 5 cm we can use the apothem to calculate the length of a side.
In a regular pentagon the apothem and radius are related by the equation:
Radius = (Side length) / (2 * tan(π/5))
Since the radius is given as 5 cm we can rearrange the equation to solve for the side length:
Side length = 2 * tan(π/5) * Radius
Side length = 2 * tan(π/5) * 5 cm
Using a calculator we can find that tan(π/5) is approximately 0.7265.
Side length ≈ 2 * 0.7265 * 5 cm
Side length ≈ 7.265 cm
The perimeter of a regular pentagon can be calculated by multiplying the side length by 5:
Perimeter = Side length * 5
Perimeter ≈ 7.265 cm * 5
Perimeter ≈ 36.325 cm
Therefore, in this case, it is concluded that the perimeter of the pentagon is approximately 36.3 cm. Option C.
Learn more about Pentagon here: https://brainly.com/question/29673128
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