Area and Perimeter of a Rhombus: Formula, Examples, and Common Mistakes

After rectangles, squares, triangles, circles, parallelograms, and trapezoids, the rhombus is the next shape in the series. You'll recognize a rhombus easily — it's the classic "diamond" shape seen in kites, playing cards, and tile patterns. It's also a frequent topic in geometry exams, especially because it introduces a new way to calculate area: using diagonals.

What Is a Rhombus?

A rhombus is a four-sided shape (quadrilateral) where:

• All four sides are equal in length
• Opposite sides are parallel
• Opposite angles are equal
• The two diagonals bisect each other at right angles (90 degrees)

A rhombus is actually a special type of parallelogram — one where all sides happen to be equal, just like a square is a special rectangle. The key measurements needed for a rhombus are its two diagonals (d₁ and d₂) for area, and its side length (s) for perimeter.

Area of a Rhombus

The area of a rhombus tells you how much surface it covers. The most common method uses the two diagonals.

Formula:

Area = ½ × diagonal 1 × diagonal 2

Or simply: A = (d₁ × d₂) ÷ 2

This formula works because the two diagonals of a rhombus cross each other at a right angle and split the shape into four equal right triangles. Multiplying the diagonals and dividing by 2 adds up the area of all four triangles at once.

Example 1:

A rhombus has diagonals of 10 cm and 8 cm. Find its area.

• Area = (d₁ × d₂) ÷ 2
• Area = (10 × 8) ÷ 2
• Area = 80 ÷ 2
• Area = 40 cm²

As always, area is measured in square units (cm², m², ft²).

Alternative method: If you know the base and perpendicular height instead of the diagonals, you can also use Area = base × height, the same formula used for a parallelogram.

Perimeter of a Rhombus

The perimeter is the total distance around all four sides. Since every side of a rhombus is equal, the formula is simple.

Formula:

Perimeter = 4 × side

Or simply: P = 4s

Example 2:

A rhombus has a side length of 9 cm. Find its perimeter.

• Perimeter = 4 × s
• Perimeter = 4 × 9
• Perimeter = 36 cm

Perimeter is measured in linear units (cm, m, ft), just like with a square.

Area vs. Perimeter: What's the Difference?

Area:

• What it measures: the space inside the rhombus
• Formula: (d₁ × d₂) ÷ 2, or base × height
• Unit: square units (cm², m²)
• What you need: both diagonals, or base and perpendicular height

Perimeter:

• What it measures: the distance around the rhombus
• Formula: 4 × side
• Unit: linear units (cm, m)
• What you need: just one side length, since all sides are equal

Common Mistakes Students Make

• Forgetting to divide by 2 in the diagonal formula. Multiplying the diagonals without dividing by 2 gives exactly double the correct area.
• Using the diagonals in the perimeter formula. The diagonals are only needed for area — perimeter only needs the side length.
• Mixing up a rhombus with a square. All rhombus sides are equal, but its angles don't have to be 90 degrees like a square's. Don't assume a rhombus has right angles unless it's stated.
• Dropping the square unit for area. Writing "40 cm" instead of "40 cm²" is a common exam mistake.

Practice Problem

Try this one yourself before checking the answer:

A rhombus-shaped garden plot has diagonals of 16 meters and 12 meters. Each side of the plot measures 10 meters. Find both its area and perimeter.

Click to see the answer

Area = (16 × 12) ÷ 2 = 192 ÷ 2 = 96 m²

Perimeter = 4 × 10 = 40 m

Quick Recap

• Area = (d₁ × d₂) ÷ 2 — measured in square units, using the two diagonals
• Perimeter = 4 × side — measured in linear units, since all four sides are equal
• A rhombus is a special parallelogram with equal sides, but its angles aren't necessarily 90 degrees

With rectangles, squares, triangles, circles, parallelograms, trapezoids, and now rhombuses covered, you've built a complete foundation across the most common 2D shapes in school geometry. From here, the natural next step is moving into 3D shapes — starting with cubes and cuboids.