Rhombus

A rhombus is a four-sided figure (quadrilateral) in which all four sides have the same length. It is a special type of parallelogram — opposite sides are parallel — so it inherits every parallelogram property: opposite angles are equal, consecutive angles are supplementary (sum to 180°), and the four interior angles always total 360°.

The diagonals are what make a rhombus special. They bisect each other at right angles, and each diagonal bisects the pair of vertex angles it connects. The perpendicular diagonals split the rhombus into four congruent right triangles, which is why the Pythagorean theorem shows up so often in rhombus problems: half of each diagonal forms the legs of a right triangle whose hypotenuse is a side of the rhombus.

Area can be computed two ways: base × height (like any parallelogram), or one half the product of the diagonals, A = (d₁ × d₂) / 2. A rhombus with diagonals of 6 and 8 has area 24, and each side is √(3² + 4²) = 5. The perimeter is simply 4 times the side length. It helps to place the rhombus in the quadrilateral family tree: every square is a rhombus with four right angles, and every rhombus is a parallelogram — but a rhombus need not be a square, and a rectangle is only a rhombus when it's a square.

Rhombus geometry appears on the ACT, GRE, and CLT math sections, typically through diagonal-based area questions, angle chasing with the bisected vertex angles, or classification questions about which quadrilateral properties a rhombus does and doesn't have.