The area formula
A = D × d ÷ 2
Where the formula comes from
The diagonals of a rhombus are perpendicular bisectors, so they cut it into four identical right triangles with legs D/2 and d/2. Each has area D·d/8, and four of them make D·d/2. The side is the hypotenuse of one of those triangles, √((D/2)² + (d/2)²).
A worked example, step by step
A rhombus with diagonals of 8 cm and 6 cm
- Area: 8 × 6 ÷ 2 = 24 cm².
- Half-diagonals: 4 cm and 3 cm.
- Side: √(4² + 3²) = 5 cm.
- Perimeter: 4 × 5 = 20 cm.
Watch the units: area is always in square units.
Where it turns up in practice
Tiling and parquet patterns, diamond-plate flooring, and kite design. The rhombus is also the unit cell of several crystal structures, and its diagonal formula is the standard way to find the area of any quadrilateral with perpendicular diagonals.