Long Diagonal Of Rhombus Given Perimeter Calculator

Formula Used:

\[ Long Diagonal of Rhombus = \frac{Perimeter of Rhombus}{2} \times \cos\left(\frac{Acute Angle of Rhombus}{2}\right) \] \[ d_{Long} = \frac{P}{2} \times \cos\left(\frac{\angle_{Acute}}{2}\right) \]

Long Diagonal of Rhombus:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Long Diagonal of Rhombus?

The Long Diagonal of a Rhombus is the longer line that connects two opposite vertices (corners) 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:

\[ Long Diagonal = \frac{Perimeter}{2} \times \cos\left(\frac{Acute Angle}{2}\right) \]

Where:

\( Perimeter \) — Total distance around the rhombus (m)
\( Acute Angle \) — Angle inside the rhombus less than 90 degrees (°)
\( \cos \) — Cosine trigonometric function

Explanation: This formula calculates the long diagonal by relating the perimeter and the acute angle of the rhombus using trigonometric relationships.

3. Importance of Long Diagonal Calculation

Details: Calculating the long diagonal is important in geometry for determining various properties of a rhombus, including area calculations and understanding its symmetrical properties.

4. Using the Calculator

Tips: Enter the perimeter in meters and the acute angle in degrees. The angle must be between 0 and 90 degrees, and the perimeter must be a positive value.

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 bisect the interior angles.

Q2: Can I calculate the area using the long diagonal?
A: Yes, the area of a rhombus can be calculated as (d1 × d2)/2, where d1 and d2 are the lengths of the diagonals.

Q3: What if I have the side length instead of perimeter?
A: Since perimeter = 4 × side, you can calculate the perimeter first if you know the side length.

Q4: Does this formula work for all types of rhombuses?
A: Yes, this formula applies to all rhombuses, including squares (which are a special type of rhombus).

Q5: How accurate is this calculation?
A: The calculation is mathematically exact based on the input values, assuming the shape is a perfect rhombus.