rhombus

A rhombus is a quadrilateral with all four sides equal in length. It is a type of parallelogram, so opposite sides are parallel and opposite angles are equal. The shape may be slanted; unlike a square, its interior angles are not necessarily right angles.

Key properties: All four sides equal; opposite sides parallel; diagonals intersect at right angles and bisect each other; diagonals also bisect the interior angles of the rhombus.

Area and perimeter: The perimeter is four times the side length. If the side length is a, the area can be found as base times height, or as half the product of the diagonals: Area = (d1*d2)/2. Equivalently, if the side length is a and the interior angle is θ, Area = a^2 sin θ.

Relations and examples: A square is a rhombus with all angles right. The rhombus is a special case of both a parallelogram and a kite. Rhombuses are common in tiling patterns and in diamond shapes used in design and playing cards.