Area Of Rectangle Given Diameter Of Circumcircle And Obtuse Angle Between Diagonals Calculator

Formula Used:

\[ A = D_c^2 \times \sin\left(\frac{\angle d_{\text{Obtuse}}}{2}\right) \times \cos\left(\frac{\angle d_{\text{Obtuse}}}{2}\right) \]

Area of Rectangle:

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1. What is the Area of Rectangle Formula?

This formula calculates the area of a rectangle using the diameter of its circumcircle and the obtuse angle between its diagonals. It provides an alternative method to the standard length × width calculation.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = D_c^2 \times \sin\left(\frac{\angle d_{\text{Obtuse}}}{2}\right) \times \cos\left(\frac{\angle d_{\text{Obtuse}}}{2}\right) \]

Where:

\( A \) — Area of Rectangle (m²)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)
\( \angle d_{\text{Obtuse}} \) — Obtuse Angle between Diagonals of Rectangle (degrees)

Explanation: The formula utilizes trigonometric relationships between the circumcircle diameter, the angle between diagonals, and the resulting area of the rectangle.

3. Importance of Area Calculation

Details: Calculating area is fundamental in geometry, architecture, engineering, and various practical applications where rectangular spaces need to be measured or designed.

4. Using the Calculator

Tips: Enter the diameter of the circumcircle in meters and the obtuse angle between diagonals in degrees (between 90° and 180°). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why use this formula instead of length × width?
A: This formula is useful when you know the circumcircle properties and angle between diagonals but not the side lengths of the rectangle.

Q2: What is a circumcircle of a rectangle?
A: A circumcircle is a circle that passes through all four vertices of the rectangle. For a rectangle, the diameter of the circumcircle equals the length of the diagonal.

Q3: Why is the angle between diagonals important?
A: The diagonals of a rectangle intersect at their midpoint and create two pairs of equal angles - one acute and one obtuse. The obtuse angle helps determine the rectangle's proportions.

Q4: Can this formula be used for squares?
A: Yes, for a square (which is a special rectangle), the angle between diagonals is 90°, and the formula still applies correctly.

Q5: What are the limitations of this formula?
A: The formula requires knowing both the circumcircle diameter and the obtuse angle between diagonals, which might not always be available in practical situations.