Rhombus Calculator

How to Calculate Rhombus Properties

A rhombus is a quadrilateral with four equal sides. It has several unique properties that make it an interesting shape to study in geometry. Let's explore how to calculate its various properties.

Rhombus Formulas

The key formulas for calculating rhombus properties are:

• Area (A) = (d₁ × d₂) / 2, where d₁ and d₂ are the diagonals
• Perimeter (P) = 4s, where s is the side length
• Acute Angle (θ) = 2 × arctan(d₂ / d₁)
• Obtuse Angle (φ) = 180° - θ

Calculation Steps

1. Measure or identify the side length and diagonals of the rhombus.
2. To calculate the area:
   • Multiply the lengths of the two diagonals.
   • Divide the result by 2.
3. To calculate the perimeter:
   • Multiply the side length by 4.
4. To calculate the angles:
   • For the acute angle, use the formula: θ = 2 × arctan(d₂ / d₁).
   • For the obtuse angle, subtract the acute angle from 180°.

Example Calculation

Let's calculate the properties of a rhombus with side length 5 units and diagonals 6 units and 8 units:

1. Given: Side length (s) = 5 units, Diagonal 1 (d₁) = 6 units, Diagonal 2 (d₂) = 8 units
2. Calculate area: A = (d₁ × d₂) / 2 = (6 × 8) / 2 = 24 square units
3. Calculate perimeter: P = 4s = 4 × 5 = 20 units
4. Calculate acute angle: θ = 2 × arctan(d₂ / d₁) = 2 × arctan(8 / 6) ≈ 106.26°
5. Calculate obtuse angle: φ = 180° - θ = 180° - 106.26° ≈ 73.74°

Visual Representation

This diagram illustrates a rhombus with its side, diagonals (d₁ and d₂), and angles (θ and φ). The rhombus is drawn in blue, while the diagonals are shown in red. The side length determines the size of the rhombus, and the diagonals intersect at the center, forming four congruent triangles.