By Claire Gillespie – Updated Mar 24, 2022

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A rhombus is a special type of parallelogram where all four sides are equal in length. It’s often seen as the diamond shape on a playing card. Understanding how to determine its height—also known as the altitude—is essential for many geometry problems and real‑world applications.

TL;DR

To find the height of a rhombus, use height = area ÷ base. If you only know the diagonals, first compute the area with area = (d₁ × d₂) ÷ 2 and then apply the same division.

Key Properties of a Rhombus

• All sides are congruent.
• Opposite angles are equal.
• Diagonals are perpendicular bisectors of each other.
• The height is the shortest distance between any two opposite sides.

Finding Height from Area and Base

The most direct method is height = area ÷ base. Because every side of a rhombus is the same length, knowing the base automatically gives you the length of all sides. For example:

• Area = 64 cm², Base = 8 cm → Height = 64 ÷ 8 = 8 cm.
• Area = 1 000 in², Base = 20 in → Height = 1 000 ÷ 20 = 50 in.

Finding Height from Diagonals

When only the diagonals are known, first compute the area using area = (d₁ × d₂) ÷ 2. Then divide by the base:

• d₁ = 4 cm, d₂ = 6 cm → Area = (4 × 6) ÷ 2 = 12 cm².
• Base = 2 cm → Height = 12 ÷ 2 = 6 cm.

These formulas hold true regardless of the units of measurement or the rhombus’s size.

For a deeper dive into rhombus properties and proofs, see Wolfram MathWorld – Rhombus.