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The Perimeter of Concave Regular Pentagon is the total length of all the boundary lines of the Concave Regular Pentagon. It represents the sum of the lengths of all five sides of this geometric shape.
The calculator uses the formula:
Where:
Explanation: This formula calculates the perimeter of a concave regular pentagon based on the distance between its two upper tips, using the mathematical constant related to the golden ratio.
Details: The formula uses the mathematical relationship between the distance of tips and the perimeter in a concave regular pentagon. The constant \( \frac{10}{1+\sqrt{5}} \) is derived from the geometric properties of this specific shape.
Tips: Enter the distance between the tips of the concave regular pentagon in meters. The value must be positive and greater than zero.
Q1: What is a concave regular pentagon?
A: A concave regular pentagon is a five-sided polygon where all sides are equal in length, but at least one interior angle is greater than 180 degrees, causing the shape to "cave in."
Q2: How is this different from a convex pentagon?
A: In a convex pentagon, all interior angles are less than 180 degrees and all vertices point outward, while a concave pentagon has at least one interior angle greater than 180 degrees.
Q3: What are typical applications of this calculation?
A: This calculation is useful in geometry, architectural design, and various engineering applications where pentagonal shapes with concave properties are used.
Q4: Can this formula be used for irregular pentagons?
A: No, this specific formula only applies to regular concave pentagons where all sides are equal and the shape has specific symmetrical properties.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect regular concave pentagons, though real-world measurements may introduce some degree of error.