Long Diagonal Of Rhombus Given Area Calculator

Formula Used:

\[ \text{Long Diagonal of Rhombus} = \frac{\text{Area of Rhombus}}{\text{Side of Rhombus} \times \sin(\frac{\text{Acute Angle of Rhombus}}{2})} \] \[ d_{Long} = \frac{A}{S \times \sin(\frac{\angle_{Acute}}{2})} \]

Long Diagonal of Rhombus:

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1. What is the Long Diagonal of Rhombus?

The Long Diagonal of a Rhombus is the longer of the two diagonals that connect opposite vertices of the rhombus. It bisects the acute angles and is perpendicular to the short diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ d_{Long} = \frac{A}{S \times \sin(\frac{\angle_{Acute}}{2})} \]

Where:

\( d_{Long} \) — Long Diagonal of Rhombus (m)
\( A \) — Area of Rhombus (m²)
\( S \) — Side of Rhombus (m)
\( \angle_{Acute} \) — Acute Angle of Rhombus (degrees)
\( \sin \) — Sine trigonometric function

Explanation: The formula calculates the long diagonal using the area, side length, and acute angle of the rhombus through trigonometric relationships.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is essential for understanding the geometric properties of a rhombus, construction applications, and solving various geometric problems involving rhombuses.

4. Using the Calculator

Tips: Enter area in square meters, side length in meters, and acute angle in degrees (must be between 0-90°). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between diagonals in a rhombus?
A: The diagonals of a rhombus are perpendicular bisectors of each other and they divide the rhombus into four congruent right triangles.

Q2: Can I calculate the long diagonal if I know both diagonals?
A: Yes, if you know both diagonals, the long diagonal is simply the longer of the two diagonal measurements.

Q3: How does the acute angle affect the long diagonal?
A: As the acute angle decreases, the long diagonal becomes longer relative to the side length, making the rhombus more elongated.

Q4: What are the units for the inputs and outputs?
A: The calculator uses meters for length measurements and square meters for area. The angle is in degrees.

Q5: Can this formula be used for squares?
A: Yes, since a square is a special type of rhombus with all angles equal to 90°, the formula works for squares as well.