Area Of Pentagon Given Perimeter Calculator

Pentagon Area Formula:

\[ A = \frac{P^2 \times \sqrt{25 + (10 \times \sqrt{5})}}{100} \]

Area of Pentagon:

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1. What is the Pentagon Area Formula?

The formula calculates the area of a regular pentagon given its perimeter. A regular pentagon has all sides equal and all interior angles equal (108° each).

2. How Does the Calculator Work?

The calculator uses the pentagon area formula:

\[ A = \frac{P^2 \times \sqrt{25 + (10 \times \sqrt{5})}}{100} \]

Where:

\( A \) — Area of pentagon
\( P \) — Perimeter of pentagon
\( \sqrt{} \) — Square root function

Explanation: This formula derives from the relationship between the perimeter and area of a regular pentagon, using the mathematical constant related to the golden ratio.

3. Importance of Pentagon Area Calculation

Details: Calculating the area of a pentagon is important in geometry, architecture, engineering, and various design applications where pentagonal shapes are used.

4. Using the Calculator

Tips: Enter the perimeter of the pentagon in meters. The value must be positive and greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: Does this formula work for irregular pentagons?
A: No, this formula is specifically for regular pentagons where all sides and angles are equal.

Q2: What are the units of measurement?
A: The perimeter should be entered in meters, and the area result will be in square meters (m²).

Q3: Can I use this for pentagonal prisms?
A: This formula calculates the area of a two-dimensional pentagon, not the surface area of a three-dimensional pentagonal prism.

Q4: What is the significance of the constants in the formula?
A: The constants derive from the geometric properties of a regular pentagon and its relationship to the golden ratio.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for regular pentagons, with accuracy limited only by the precision of the input values and computational rounding.