Geometry

Question Analysis

The main focus of this question is two - fold. First, it explores the relationship between the number of sides and the perimeter of a regular polygon, which tests the understanding of the basic property of regular polygons where all sides are equal. Second, it requires calculating the measure of one interior angle of a regular hexagon, which involves applying the formula for interior angles of regular polygons.

 

Key Concept Explanation

Relationship between number of sides () and perimeter () of a regular polygon: In a regular polygon, all sides have the same length . The perimeter is the sum of the lengths of all sides. So, , meaning the perimeter is directly proportional to the number of sides when the side - length is constant.

- Measure of an interior angle () of a regular polygon: The formula to find the measure of an interior angle of a regular polygon with sides is .

 

Step - by - Step Solution

1. Relationship between number of sides and perimeter:

Let the side - length of a regular polygon be . If the number of sides is , then by adding the lengths of all equal - length sides, we get .

Using the concept of multiplication as repeated addition, . For example, if a regular triangle (equilateral triangle) has side - length units and , then units.

2. Measure of one interior angle of a regular hexagon:

For a hexagon, .

Substitute into the formula .

First, calculate :

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