Diamond (Rhombus) — Definition, Formula & Examples

A diamond is the everyday name for a rhombus — a flat shape with four straight sides that are all the same length. It looks like a square tilted to the side.

A rhombus is a quadrilateral in which all four sides are congruent. Its opposite angles are equal, and its diagonals bisect each other at right angles.

Key Formula

A = \frac{d_1 \times d_2}{2}

Where:

$A$ = Area of the rhombus
$d_1$ = Length of the first diagonal
$d_2$ = Length of the second diagonal

How It Works

To identify a diamond (rhombus), check that all four sides have equal length. Opposite sides are parallel, just like a parallelogram, but a rhombus adds the rule that every side must be the same length. The two diagonals (lines connecting opposite corners) always cross at 90°. You can find the area by multiplying the two diagonal lengths and dividing by 2.

Worked Example

Problem: A diamond-shaped kite has diagonals that measure 6 cm and 8 cm. What is its area?

Step 1: Write down the diagonal lengths.

d_1 = 6 \text{ cm}, \quad d_2 = 8 \text{ cm}

Step 2: Multiply the diagonals and divide by 2.

A = \frac{6 \times 8}{2} = \frac{48}{2} = 24 \text{ cm}^2

Answer: The area of the diamond is 24 cm².

Why It Matters

Rhombus shapes appear in tile patterns, road signs, and playing cards. Understanding diamonds helps build a foundation for classifying quadrilaterals in later geometry courses.

Common Mistakes

Mistake: Thinking a square is not a rhombus.

Correction: A square is a special type of rhombus where all four angles are also 90°. Every square is a rhombus, but not every rhombus is a square.