1. What is the Perimeter of Decagon Formula?

The perimeter of a decagon can be calculated from its area using the formula: \[ P = 10 \times \sqrt{\frac{2 \times A}{5 \times \sqrt{5 + (2 \times \sqrt{5})}}} \] This formula provides the total distance around the edge of a regular decagon when the area is known.

2. How Does the Calculator Work?

The calculator uses the perimeter formula:

Where:

• \( P \) — Perimeter of the decagon (m)
• \( A \) — Area of the decagon (m²)
• \( \sqrt{} \) — Square root function

Explanation: The formula derives the perimeter from the area by reversing the standard area calculation formula for a regular decagon.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter from area is useful in various geometric applications, construction projects, and mathematical problems where the area is known but the perimeter is needed for further calculations.

4. Using the Calculator

Tips: Enter the area of the decagon in square meters. The value must be positive and greater than zero for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is a regular decagon?
A: A regular decagon is a ten-sided polygon where all sides are equal in length and all interior angles are equal (144 degrees each).

Q2: Does this formula work for irregular decagons?
A: No, this formula is specifically for regular decagons where all sides and angles are equal.

Q3: What are the units for the result?
A: The perimeter result will be in the same linear unit as the square root of the area unit (e.g., if area is in m², perimeter will be in m).

Q4: What is the relationship between area and perimeter?
A: For regular polygons, there is a mathematical relationship between area and perimeter that can be derived from geometric principles.

Q5: Can this formula be used for other polygons?
A: No, this specific formula is only applicable to regular decagons. Other polygons have different area-perimeter relationships.