Perimeter of Rectangle given Area and Angle between Diagonal and Breadth Calculator

Perimeter of Rectangle Formula:

\[ P = 2 \times \sqrt{(A \times \sec(\angle_{db}) \times \csc(\angle_{db})) + (2 \times A)} \]

Perimeter of Rectangle (P):

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1. What is the Perimeter of Rectangle Formula?

The perimeter of a rectangle given area and angle between diagonal and breadth is calculated using a specialized formula that incorporates trigonometric functions to determine the total boundary length based on the area and the specified angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times \sqrt{(A \times \sec(\angle_{db}) \times \csc(\angle_{db})) + (2 \times A)} \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( A \) — Area of Rectangle (m²)
\( \angle_{db} \) — Angle between Diagonal and Breadth (degrees)
\( \sec \) — Secant trigonometric function
\( \csc \) — Cosecant trigonometric function

Explanation: The formula calculates the perimeter by first determining the relationship between the area, the given angle, and the rectangle's dimensions using trigonometric identities.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is essential in various fields including construction, landscaping, and manufacturing. It helps determine the amount of material needed for fencing, framing, or bordering a rectangular area.

4. Using the Calculator

Tips: Enter the area in square meters and the angle between diagonal and breadth in degrees. The angle must be between 0 and 90 degrees. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for perimeter calculation?
A: This formula is particularly useful when you know the area of the rectangle and the angle between the diagonal and breadth, but not the individual length and width dimensions.

Q2: What is the range of valid angle values?
A: The angle between diagonal and breadth must be between 0 and 90 degrees (exclusive of 0).

Q3: Can this calculator handle different units?
A: The calculator uses meters for length and square meters for area. For other units, convert your measurements to these units before calculation.

Q4: What if I get an error in calculation?
A: Ensure that both area and angle values are positive numbers, and the angle is between 0 and 90 degrees.

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, providing precision suitable for most practical applications.