Definition: A rhombus is a parallelogram with four congruent sides; its diagonals are perpendicular and bisect the angles at the vertices they join.
What makes a rhombus special?
It has every parallelogram property, plus four equal sides. Its diagonals cross at right angles and cut each other in half. Each diagonal bisects a pair of opposite angles.
How do you compute its area?
Area = (1/2) · d1 · d2, where d1 and d2 are the diagonals. The perpendicular diagonals cut the rhombus into four congruent right triangles, which lets you find the side with the Pythagorean theorem.
Example. A rhombus has diagonals 16 and 30. The area is (1/2)(16)(30) = 240. Half-diagonals are 8 and 15, so each side is the square root of 64 + 225 = 289, which is 17. The perimeter is 4(17) = 68.
What mistakes are frequent?
Treating a rhombus as a square: it only has equal sides, and its angles are generally not right angles. Using base times side instead of base times height also fails. A square is a rhombus with right angles, but not every rhombus is a square.