Properties of a Rhombus (PDF)

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					                     Properties of a Rhombus
Properties of a Rhombus

A Rhombus is four - sided figure that is a special type of quadrilateral. It is sometimes
represented by ‘◊’ symbol. A Rhombus is a convex parallelogram in which every one of the
four sides are equivalent in magnitude. It is a diamond shape figure as shown in the figure
below:

The Properties of a Rhombus make it special if compared to a simple parallelogram. We have
described these Properties of a Rhombus using a particular ◊ ABCD in the following
subdivision:

1. A rhombus is sometimes called an equilateral quadrilateral, as all its four sides are equal. In
other words we can write : AB = BC = CD = DA.

2. Every rhombus can be considered to b a parallelogram but vice versa is not true. Thus, all
properties that hold true for a general parallelogram are also true for a rhombus. Thus,
opposite sides are parallel and equal. Opposite angles are also identical in degrees.

3. A rhombus is similar to a square if we take into account the facts that all sides are equal
and opposite sides are parallel. However, the difference is that all angles of a square are
equal and their measurement is 90o.
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Thus, a square is a special case of a rhombus. In addition, out of all possible rhombuses of
equivalent sides, a square has maximum area.

4. The diagonals (i.e. lines AC and DB) bisect the angles they contain (i.e. AC cuts in half
angles A and C and diagonal BD bisects angles B and D).

Additionally, they also divide each other in exact halves. At the point of intersection of
diagonals, four 90o angles are formed. As a result, we can conclude that diagonals in a
rhombus bisect each other at 90o.

A point to be noted is that the diagonals may or may not be equal. If the diagonals are equal in
a rhombus, then it is essentially a square.

5. To find perimeter of a rhombus simply sum up the magnitudes of all four sides or multiply
the magnitude of a side with 4. We can write:

Perimeter of a rhombus = AB + BC + CD + DA,

If AB = BC = CD = DA = x, then,

Perimeter of a rhombus = 4 x.

6. There are various ways to find the area of a rhombus. If its height and length of a base are
known then area is calculated as follows:

Area of a rhombus = (base * height) / 2,

I.e. if base = x and height = y, then,

Area of a rhombus = (x * y) / 2,

If the lengths of the diagonals are known then area is calculated as follows:
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Area of a rhombus = (diagonal1 * diagonal2) / 2,

Where, diagonal1 and diagonal2 are lengths of two diagonals AC and BD.

7.      The sum of the adjacent angles in a rhombus is equal to 180o.

∠ A + ∠ B = 180o,

∠ C + ∠ D = 180o,

8. In a rhombus, the total sum of the squares of the sides (consider length of each side to be x
units) is the same as the total sum of the squares of the diagonals (consider the length of
diagonal1 to be d1 units and the length of diagonal2 to be d2 units). Mathematically, it can be
written as:

d12 + d22 = 4 x2,




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