What is a Rhombus?
A rhombus is a quadrilateral (four-sided polygon) where all four sides are equal in length. It is a special type of parallelogram. The diagonals of a rhombus bisect each other at right angles, and opposite angles are equal.
Rhombus Area Formulas
Using Diagonals
When both diagonals are known, the area is half their product.
A = (d1 x d2) / 2
Using Side and Height
Like any parallelogram, area equals base times height.
A = s x h
Using Side and Angle
Using the sine of an interior angle with the side length squared.
A = s² x sin(theta)
Perimeter of a Rhombus
Since all sides of a rhombus are equal, the perimeter is simply four times the side length: P = 4s. When only diagonals are known, you can find the side using the Pythagorean theorem: s = sqrt((d1/2)² + (d2/2)²).
Properties of a Rhombus
- All four sides are equal in length.
- Opposite angles are equal.
- Diagonals bisect each other at right angles (90 degrees).
- Each diagonal bisects a pair of opposite angles.
- The sum of two adjacent angles is 180 degrees.
- A square is a special case of a rhombus where all angles are 90 degrees.
Real-World Applications
- Diamond shapes in jewelry and design follow rhombus geometry.
- Kite designs often incorporate rhombus shapes.
- Tile patterns and floor designs frequently use rhombus shapes.
- Road signs (diamond-shaped warning signs) are rhombi.