Perimeter of Rectangle given Diameter of Circumcircle and Acute Angle between Diagonals Calculator

Formula Used:

\[ P = 2 \times D_c \times \sqrt{1 + (2 \times \sin(\frac{\angle_{d(Acute)}}{2}) \times \cos(\frac{\angle_{d(Acute)}}{2}))} \]

Perimeter of Rectangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Perimeter of Rectangle given Diameter of Circumcircle and Acute Angle between Diagonals?

This calculation determines the perimeter of a rectangle when the diameter of its circumcircle and the acute angle between its diagonals are known. The circumcircle is the circle that passes through all four vertices of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P = 2 \times D_c \times \sqrt{1 + (2 \times \sin(\frac{\angle_{d(Acute)}}{2}) \times \cos(\frac{\angle_{d(Acute)}}{2}))} \]

Where:

\( P \) — Perimeter of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle_{d(Acute)} \) — Acute Angle between Diagonals of Rectangle (degrees)

Explanation: The formula relates the perimeter of a rectangle to the diameter of its circumcircle and the acute angle between its diagonals using trigonometric functions.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a rectangle is fundamental in geometry and has practical applications in construction, design, and various engineering fields where rectangular shapes are involved.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the acute angle between diagonals in degrees (0-90°). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of a rectangle. For a rectangle, the center of the circumcircle is at the intersection point of the diagonals.

Q2: Why is the angle between diagonals important?
A: The angle between diagonals affects the aspect ratio of the rectangle. Different angles correspond to rectangles with different length-to-width ratios.

Q3: What is the range of possible acute angles between diagonals?
A: For a rectangle, the acute angle between diagonals ranges from 0° to 90°, with 90° representing a square.

Q4: Can this formula be used for other quadrilaterals?
A: No, this specific formula applies only to rectangles, as it relies on the unique properties of rectangles and their circumcircles.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect rectangles. The accuracy depends on the precision of the input values.