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The edge length of a concave regular pentagon is the measurement of any side of this unique geometric shape. A concave regular pentagon has all sides equal in length but has at least one interior angle greater than 180 degrees, creating a "caved-in" appearance.
The calculator uses the mathematical formula:
Where:
Explanation: This formula derives from the geometric properties of regular pentagons and the specific characteristics of concave pentagons, relating the area directly to the edge length through mathematical constants.
Details: Calculating the edge length is essential for geometric construction, architectural design, and mathematical analysis of pentagonal shapes. It helps in determining proportions and scaling properties of concave pentagonal structures.
Tips: Enter the area of the concave regular pentagon in square meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length.
Q1: What makes a pentagon "concave"?
A: A concave pentagon has at least one interior angle greater than 180 degrees, causing the shape to appear "caved in" or indented.
Q2: How is this different from a regular convex pentagon?
A: While both have equal side lengths, a convex pentagon has all interior angles less than 180 degrees, creating an outward-bulging shape.
Q3: What are practical applications of this calculation?
A: This calculation is used in architectural design, tile patterns, mathematical research, and geometric art projects involving pentagonal shapes.
Q4: Can this formula be used for any pentagon?
A: No, this specific formula applies only to regular concave pentagons where all sides are equal and the shape has the specific concave properties.
Q5: What units should I use for the area input?
A: The calculator expects area in square meters, but you can use any consistent unit system as long as the edge length output is interpreted in the same linear units.