Area of Concave Regular Pentagon given Perimeter Calculator

Area of Concave Regular Pentagon Formula:

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

Area of Concave Regular Pentagon:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Area of Concave Regular Pentagon?

The Area of Concave Regular Pentagon is the total quantity of plane enclosed by the boundary of the Concave Regular Pentagon. It represents the two-dimensional space contained within the pentagon's boundaries.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( A \) — Area of Concave Regular Pentagon (m²)
\( P \) — Perimeter of Concave Regular Pentagon (m)
\( \sqrt{} \) — Square root function

Explanation: This formula calculates the area of a concave regular pentagon based on its perimeter, using mathematical constants derived from the pentagon's geometric properties.

3. Importance of Area Calculation

Details: Calculating the area of geometric shapes is fundamental in mathematics, engineering, architecture, and various scientific fields. It helps in material estimation, space planning, and structural analysis.

4. Using the Calculator

Tips: Enter the perimeter of the concave regular pentagon in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is a concave regular pentagon?
A: A concave regular pentagon is a five-sided polygon with equal sides and angles, but with at least one interior angle greater than 180 degrees, causing it to "cave inwards."

Q2: How does this differ from a convex pentagon area calculation?
A: Concave pentagons have a more complex area calculation due to their inward-bending nature, requiring specialized formulas that account for the concave regions.

Q3: What units should I use for the perimeter?
A: The perimeter should be in meters, and the resulting area will be in square meters (m²). You can convert from other units before input.

Q4: Can this formula be used for irregular pentagons?
A: No, this formula is specifically designed for regular concave pentagons. Irregular pentagons require different calculation methods.

Q5: What is the precision of the calculation?
A: The calculator provides results with 6 decimal places precision, suitable for most practical applications in engineering and mathematics.