Rhombus Area Calculator
Calculate the area of a rhombus using its diagonals: A = (d₁ × d₂) / 2
Enter Diagonals
Step-by-Step Solution:
1. Formula: Area = (d₁ × d₂) / 2
2. Multiply diagonals: 10 × 8 = 80
3. Divide by 2: 80 / 2 = 40.00 square units
Rhombus Area Formula
Area = (d₁ × d₂) / 2
where: - d₁ = length of the first diagonal - d₂ = length of the second diagonal
How to Calculate Rhombus Area
- Measure the first diagonal (d₁): The distance between one pair of opposite vertices
- Measure the second diagonal (d₂): The distance between the other pair of opposite vertices
- Multiply the diagonals: Calculate d₁ × d₂
- Divide by 2: The area is half the product of the diagonals
Why the Formula Works
The diagonals of a rhombus bisect each other at right angles, dividing the rhombus into four right triangles. Each triangle has legs of length d₁/2 and d₂/2. The total area of the four triangles equals (d₁ × d₂) / 2.
Real-World Applications
Rhombus calculations are used in: - Tiling and flooring: Diamond-shaped tile patterns - Crystal structures: Rhombic crystal systems in mineralogy - Kite design: Many kites are rhombus-shaped - Graphic design: Diamond and argyle patterns - Architecture: Decorative diamond window panes
Common Questions
What is the formula for rhombus area?
The rhombus area formula using diagonals is A = (d₁ × d₂) / 2, where d₁ and d₂ are the lengths of the two diagonals.
What is the difference between a rhombus and a square?
A square is a special rhombus where all angles are 90 degrees and the diagonals are equal in length. In a general rhombus, opposite angles are equal but not necessarily 90 degrees.