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The Edge Length of Square of Concave Pentagon is the length of any edge of the square from which the Concave Pentagon is created by removing one triangle formed by the diagonals of the square. It represents the original dimension of the square before the triangular cutout.
The calculator uses the formula:
Where:
Explanation: The formula derives from the geometric relationship between the square's edge length and the leg length of the isosceles right triangle removed from the square's corner.
Details: Calculating the original square's edge length is crucial for understanding the geometric transformation, determining material requirements, and analyzing the properties of the resulting concave pentagon shape in architectural and engineering applications.
Tips: Enter the leg length of the triangle in meters. The value must be positive and greater than zero. The calculator will compute the corresponding edge length of the original square.
Q1: Why is there a √2 factor in the formula?
A: The √2 factor comes from the relationship between the leg of an isosceles right triangle and the hypotenuse, which in this case corresponds to the square's edge length.
Q2: What units should I use for the input?
A: The calculator uses meters as the default unit, but you can use any consistent unit system as long as both input and output use the same units.
Q3: Can this formula be used for any concave pentagon?
A: This specific formula applies only to concave pentagons created by removing an isosceles right triangle from a square's corner along its diagonal.
Q4: What if I know the square's edge length and want to find the triangle's leg length?
A: You can rearrange the formula: \( l_{Leg(Triangle)} = \frac{l_{e(Square)}}{\sqrt{2}} \)
Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise measurements of the triangle's leg length and perfect geometric construction.