Perimeter Of Rectangle Given Area And Angle Between Diagonal And Length Calculator

Formula Used:

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

Perimeter of Rectangle:

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1. What is the Perimeter of Rectangle Formula?

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

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula calculates the perimeter by considering the relationship between area, the specified angle, and the trigonometric properties of the rectangle.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is essential in various fields including construction, engineering, and design, where boundary measurements are crucial for material estimation and spatial planning.

4. Using the Calculator

Tips: Enter the area in square meters and the angle in degrees (between 0 and 90). All values must be valid (area > 0, angle between 0-90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle values?
A: The angle between diagonal and length must be between 0 and 90 degrees (exclusive).

Q2: Can this formula be used for squares?
A: Yes, for a square the angle between diagonal and length is 45 degrees, and the formula will correctly calculate the perimeter.

Q3: What units should be used for inputs?
A: Area should be in square meters, angle in degrees. The calculator automatically converts angle to radians for trigonometric calculations.

Q4: Why use trigonometric functions in perimeter calculation?
A: Trigonometric functions help relate the angle between diagonal and length to the side lengths, allowing perimeter calculation from area and angle alone.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values, with results rounded to 6 decimal places for clarity.