Area of Rectangle given Diagonal and Obtuse Angle between Diagonals Calculator

Formula

The formula to calculate the Area of Rectangle (A) is:

\[ A = \frac{d^2 \cdot \sin(\angle d(\text{Obtuse}))}{2} \]

Where:

\(A\) is the Area of Rectangle (measured in square meters).
\(d\) is the Diagonal of Rectangle (measured in meters).
\(\angle d(\text{Obtuse})\) is the Obtuse Angle between Diagonals of Rectangle (measured in radians).

Definition

Area of Rectangle is the total quantity of plane enclosed by the boundary of the Rectangle.

Diagonal of Rectangle is the length of the line joining any pair of opposite vertices of the Rectangle.

Obtuse Angle between Diagonals of Rectangle is the angle made by the diagonals of the Rectangle which is greater than 90 degrees.

How to calculate Area of Rectangle

Let's assume the following values:

Diagonal of Rectangle (d) = 10 meters
Obtuse Angle between Diagonals of Rectangle (∠d(Obtuse)) = 1.9198621771934 radians

Using the formula:

\[ A = \frac{10^2 \cdot \sin(1.9198621771934)}{2} \]

Evaluating:

\[ A \approx 46.9846 \, \text{square meters} \]

The Area of Rectangle is approximately 46.9846 square meters.

Conversion Chart

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Diagonal (d) (meters)	Obtuse Angle (∠d(Obtuse)) (radians)	Area (A) (square meters)