Math Problem Statement

Find the perimeter and area of a regular hexagon with side length 2 cm and apothem 1.73 cm.

Solution

To solve this problem, let's find the perimeter and area of the regular hexagon.

Given:

  • Side length s=2 cms = 2 \text{ cm}
  • Apothem a=1.73 cma = 1.73 \text{ cm}

Step 1: Perimeter

The perimeter PP of a regular hexagon is given by: P=6×sP = 6 \times s P=6×2=12 cmP = 6 \times 2 = 12 \text{ cm}

Step 2: Area

The area AA of a regular hexagon can be calculated using: A=12×P×aA = \frac{1}{2} \times P \times a A=12×12×1.73A = \frac{1}{2} \times 12 \times 1.73 A=10.38 cm2A = 10.38 \text{ cm}^2

Conclusion:

  • Perimeter (P): 12 cm
  • Area (A): 10.38 cm²

Correct Answer:

  • Perimeter: 12 cm12 \text{ cm}
  • Area: 10.38 cm210.38 \text{ cm}^2 (Option a)

Would you like a detailed explanation of any step, or do you have any questions?

Further Questions:

  1. What is the formula to find the area of a regular polygon with different numbers of sides?
  2. How does the apothem affect the area of a regular polygon?
  3. Can you derive the formula for the area of a hexagon using the triangles formed by the apothem?
  4. What would happen to the perimeter and area if the side length doubled?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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