Rhombus Area Calculator
Calculate the area, perimeter, and properties of a rhombus using various formulas
Calculate Rhombus Area
Length of the first diagonal
Length of the second diagonal
Rhombus Properties
Formula used: Area = (d₁ × d₂) / 2
Method: Using diagonal lengths
Example Calculations
Method 1: Using Diagonals
Given: Diagonal 1 = 8 units, Diagonal 2 = 10 units
Formula: Area = (d₁ × d₂) / 2
Calculation: Area = (8 × 10) / 2 = 40 square units
Side: s = √((d₁/2)² + (d₂/2)²) = √(16 + 25) = √41 ≈ 6.40 units
Perimeter: P = 4s = 4 × 6.40 = 25.61 units
Method 2: Using Side and Height
Given: Side = 5 units, Height = 4 units
Formula: Area = side × height
Calculation: Area = 5 × 4 = 20 square units
Perimeter: P = 4 × 5 = 20 units
Method 3: Using Side and Angle
Given: Side = 6 units, Angle = 30°
Formula: Area = side² × sin(angle)
Calculation: Area = 6² × sin(30°) = 36 × 0.5 = 18 square units
Perimeter: P = 4 × 6 = 24 units
Rhombus Properties
All four sides are equal in length
Opposite angles are equal
Diagonals bisect each other at right angles
Adjacent angles are supplementary (sum to 180°)
Diagonals bisect the vertex angles
Area Formulas
Using Diagonals
Area = (d₁ × d₂) / 2
Using Base & Height
Area = base × height
Using Side & Angle
Area = side² × sin(angle)
Quick Facts
A rhombus is also called a diamond shape
Every square is a rhombus (but not vice versa)
A rhombus is a special type of parallelogram
Perimeter = 4 × side length
Understanding Rhombus Area Calculation
What is a Rhombus?
A rhombus is a quadrilateral (four-sided polygon) where all four sides have equal length. It's also known as an equilateral quadrilateral or a diamond shape. While all squares are rhombuses, not all rhombuses are squares.
Key Properties
- •All sides are equal in length
- •Opposite sides are parallel
- •Opposite angles are equal
- •Diagonals bisect each other perpendicularly
Area Calculation Methods
Method 1: Diagonals
Area = (d₁ × d₂) / 2
Most common method when diagonal lengths are known
Method 2: Base and Height
Area = base × height
Used when side length and perpendicular height are known
Method 3: Side and Angle
Area = side² × sin(angle)
Useful when side length and any interior angle are known