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Semiperimeter of Cyclic Quadrilateral Formula:
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The semiperimeter of a cyclic quadrilateral is half of the total perimeter of the quadrilateral. A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a single circle.
The calculator uses the semiperimeter formula:
Where:
Explanation: The semiperimeter is simply half of the total perimeter, which is the sum of all four sides of the cyclic quadrilateral.
Details: The semiperimeter is an important parameter in various geometric formulas involving cyclic quadrilaterals, including area calculations using Brahmagupta's formula and other geometric properties.
Tips: Enter the perimeter of the cyclic quadrilateral in meters. The value must be positive and greater than zero.
Q1: What is a cyclic quadrilateral?
A: A cyclic quadrilateral is a four-sided polygon where all four vertices lie on a single circle, making it an inscribed quadrilateral.
Q2: How is semiperimeter different from perimeter?
A: The semiperimeter is exactly half of the perimeter. If the perimeter is the total distance around the quadrilateral, the semiperimeter is half of that total distance.
Q3: Why is semiperimeter important in geometry?
A: Semiperimeter is used in various geometric formulas, particularly in Brahmagupta's formula for calculating the area of a cyclic quadrilateral.
Q4: Can this calculator be used for any quadrilateral?
A: While the semiperimeter formula works for any quadrilateral, this calculator is specifically designed for cyclic quadrilaterals, though the semiperimeter calculation itself is the same for all quadrilaterals.
Q5: What units should I use for the perimeter?
A: You can use any consistent unit of length (meters, centimeters, inches, etc.), but the calculator displays results in meters by default. The result will be in the same unit as your input.