Perimeter Of Rectangle Given Area And Circumradius Calculator

Perimeter Of Rectangle Given Area And Circumradius Formula:

\[ P = 2 \times \sqrt{(2 \times A) + (4 \times rc^2)} \]

Perimeter of Rectangle (P):

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1. What is the Perimeter Of Rectangle Given Area And Circumradius Formula?

The Perimeter Of Rectangle Given Area And Circumradius formula calculates the total boundary length of a rectangle when its area and circumradius are known. This formula provides a mathematical relationship between these geometric properties of a rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times \sqrt{(2 \times A) + (4 \times rc^2)} \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( A \) — Area of Rectangle (m²)
\( rc \) — Circumradius of Rectangle (m)

Explanation: The formula derives from the geometric relationships between a rectangle's perimeter, area, and circumradius, using the Pythagorean theorem and algebraic manipulation.

3. Importance of Perimeter Calculation

Details: Calculating perimeter from area and circumradius is useful in various geometric problems, architectural design, and engineering applications where these parameters are known but the side lengths are not directly available.

4. Using the Calculator

Tips: Enter the area in square meters and circumradius in meters. Both values must be positive numbers greater than zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is circumradius of a rectangle?
A: Circumradius is the radius of the circle that passes through all four vertices of the rectangle. For a rectangle, it equals half the length of the diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special case of rectangle, this formula works for squares as well.

Q3: What are the units of measurement?
A: The calculator uses meters for length measurements and square meters for area. Ensure consistent units for accurate results.

Q4: Are there limitations to this formula?
A: The formula assumes a perfect rectangle and may not be accurate for irregular quadrilaterals or when input values are inconsistent.

Q5: How is this formula derived?
A: The formula combines the relationships: Area = length × width, Diagonal = 2 × circumradius, and Perimeter = 2 × (length + width), using the Pythagorean theorem.