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Rhombus Calculator

The Rhombus Calculator is a convenient tool to calculate the side length, angles, perimeter, and area of a rhombus by entering the lengths of its diagonals. This guide covers how to use the calculator, the formulas involved, examples, and answers to frequently asked questions.


How to Use the Rhombus Calculator

Follow these simple steps to use the Rhombus Calculator:

  • Step 1: Enter the lengths of Diagonal 1 and Diagonal 2.
  • Step 2: Click the Calculate button.
  • Step 3: The calculator will display the Side Length, Angles, Perimeter, and Area.

Formulas for Rhombus Calculator

Side Length (S)

The side length (S) of a rhombus can be calculated using half the diagonals and the Pythagorean theorem:

\( S = \sqrt{\left(\frac{\text{Diagonal 1}}{2}\right)^2 + \left(\frac{\text{Diagonal 2}}{2}\right)^2} \)

Angles (Angle A and Angle B)

In a rhombus, two opposite angles are equal, and adjacent angles are supplementary:

Angle A = \( 2 \times \arctan\left(\frac{\text{Diagonal 2}}{\text{Diagonal 1}}\right) \)

Angle B = 180° – Angle A

Perimeter (P)

The perimeter (P) of a rhombus is four times the side length:

\( P = 4 \times S \)

Area (A)

The area (A) of a rhombus is half the product of its diagonals:

\( A = \frac{\text{Diagonal 1} \times \text{Diagonal 2}}{2} \)


Examples

Example 1

Problem: Calculate the side length, angles, perimeter, and area of a rhombus with \( \text{Diagonal 1} = 10 \) units and \( \text{Diagonal 2} = 8 \) units.

Solution

Step 1: Calculate the Side Length

Use the formula for side length:

Side Length = \( \sqrt{\left(\frac{\text{Diagonal 1}}{2}\right)^2 + \left(\frac{\text{Diagonal 2}}{2}\right)^2} \)

Substitute the values:

Side Length = \( \sqrt{\left(\frac{10}{2}\right)^2 + \left(\frac{8}{2}\right)^2} = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} \approx 6.4 \) units

Answer: The side length of the rhombus is approximately 6.4 units.

Step 2: Calculate Angles

Use the formula for Angle A:

Angle \( A = 2 \times \arctan\left(\frac{\text{Diagonal 2}}{\text{Diagonal 1}}\right) \)

Substitute the values (in degrees):

Angle \( A \approx 2 \times \arctan\left(\frac{8}{10}\right) \approx 2 \times 38.66^\circ \approx 77.32^\circ \)

Angle \( B = 180^\circ – \text{Angle A} \approx 180^\circ – 77.32^\circ \approx 102.68^\circ \)

Answer: Angle A ≈ 77.32° and Angle B ≈ 102.68°.

Step 3: Calculate the Perimeter

Use the formula for perimeter:

Perimeter = \( 4 \times \text{Side Length} \)

Substitute the value:

Perimeter = \( 4 \times 6.4 \approx 25.6 \) units

Answer: The perimeter of the rhombus is approximately 25.6 units.

Step 4: Calculate the Area

Use the formula for area:

Area = \( \frac{\text{Diagonal 1} \times \text{Diagonal 2}}{2} \)

Substitute the values:

Area = \( \frac{10 \times 8}{2} = \frac{80}{2} = 40 \) square units

Answer: The area of the rhombus is 40 square units.


FAQs

1. How is the side length of a rhombus calculated?

The side length of a rhombus can be calculated using half the diagonals and the Pythagorean theorem: \( S = \sqrt{\left(\frac{\text{Diagonal 1}}{2}\right)^2 + \left(\frac{\text{Diagonal 2}}{2}\right)^2} \).

2. What is the formula for the perimeter of a rhombus?

The perimeter of a rhombus is four times the length of one side, calculated as \( P = 4 \times S \).

3. How do I find the area of a rhombus?

The area of a rhombus is half the product of its diagonals, calculated as \( A = \frac{\text{Diagonal 1} \times \text{Diagonal 2}}{2} \).