Math Problem Statement
Solution
To solve this problem, let's find the perimeter and area of the regular hexagon.
Given:
- Side length
- Apothem
Step 1: Perimeter
The perimeter of a regular hexagon is given by:
Step 2: Area
The area of a regular hexagon can be calculated using:
Conclusion:
- Perimeter (P): 12 cm
- Area (A): 10.38 cm²
Correct Answer:
- Perimeter:
- Area: (Option a)
Would you like a detailed explanation of any step, or do you have any questions?
Further Questions:
- What is the formula to find the area of a regular polygon with different numbers of sides?
- How does the apothem affect the area of a regular polygon?
- Can you derive the formula for the area of a hexagon using the triangles formed by the apothem?
- What would happen to the perimeter and area if the side length doubled?
- How can you find the apothem if only the side length is known?
Tip:
In regular polygons, knowing the side length and apothem makes calculating the area straightforward. Remember, the apothem is always perpendicular to a side.
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Math Problem Analysis
Mathematical Concepts
Geometry
Regular Polygons
Perimeter
Area
Formulas
Perimeter of a hexagon: P = 6 × side length
Area of a hexagon: A = 1/2 × Perimeter × Apothem
Theorems
Properties of Regular Polygons
Relationship between apothem and area in regular polygons
Suitable Grade Level
Grades 6-8
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