(Originais Teachy 2024) - Question Hard of Mathematics

During a practical math class, 7th grade students observed the formation of regular polygons with stretched strings. The challenge proposed by the teacher was to determine the number of sides of a polygon based on its linear measurements. The teacher explained that to measure the perimeter of the polygon, the string should be stretched around all consecutive vertices of the polygon, and then the string measurement used to find the measurement of each side. Later, the concept of circumscribed circle was introduced, which is the smallest circle in which all the vertices of the polygon touch, considering it as the 'line' that delimits the polygon. Based on this knowledge, and knowing that the radius of the circumscribed circle to a regular polygon with 10 sides measures 30 centimeters, propose an algorithm that, receiving the radius of the circumscribed circle as input, determines the perimeter of the polygon and then calculates the measurement of each of its sides. The algorithm should be written in pseudocode, detailing step by step the necessary mathematical operations to find the perimeter and the length of a side of the polygon.