Rhombus: Detailed Explanation

A rhombus is a special type of quadrilateral (four-sided figure) that is also part of the parallelogram family. It is often referred to as a “diamond” shape. Below are the key properties and details about the rhombus:

Properties of a Rhombus:

1. All sides are equal: One of the most defining characteristics of a rhombus is that all four sides are equal in length.
2. Opposite angles are equal: While the angles are not necessarily 90°, the opposite angles of a rhombus are always equal.
3. Opposite sides are parallel: Like all parallelograms, a rhombus has opposite sides that are parallel.
4. Diagonals:
   • The diagonals of a rhombus bisect each other at right angles (90°).
   • The diagonals do not have to be equal in length.
   • The diagonals bisect the internal angles of the rhombus.
5. Area and Perimeter:
   • Area = 12×Diagonal1×Diagonal2\frac{1}{2} \times \text{Diagonal}_1 \times \text{Diagonal}_221​×Diagonal1​×Diagonal2​ (The area is calculated using the lengths of the diagonals).
   • Perimeter = 4 × Side (If the side of a rhombus is ‘a,’ the perimeter is $4a$).
6. Symmetry:
   • A rhombus has two lines of symmetry: one along each diagonal.
   • A rhombus also has rotational symmetry at 180°.

Comparison of Rhombus with Other Figures:

Rhombus vs Square:

• Commonality: Both the rhombus and square have all sides equal, opposite sides parallel, and diagonals that bisect each other at 90°.
• Difference: The angles in a square are all 90°, while in a rhombus, the angles can vary. Also, the diagonals of a square are equal, while in a rhombus, they are not.

Rhombus vs Rectangle:

• Commonality: Both have opposite sides that are parallel, and both are types of parallelograms.
• Difference: In a rectangle, opposite sides are equal, but not all sides are equal like in a rhombus. The angles in a rectangle are all 90°, whereas in a rhombus, the angles can vary.

Rhombus vs Parallelogram:

• Commonality: Both have opposite sides parallel and equal, and opposite angles are equal.
• Difference: In a parallelogram, only opposite sides are equal, while in a rhombus, all four sides are equal. The diagonals of a parallelogram do not bisect each other at right angles, whereas in a rhombus, they do.

Rhombus vs Trapezium:

• Commonality: Both are quadrilaterals (four-sided figures).
• Difference: A trapezium has only one pair of parallel sides, while a rhombus has two pairs. In a trapezium, sides and angles are not necessarily equal, whereas in a rhombus, all sides are equal.

Real-Life Examples of a Rhombus:

• Diamond shape: The shape of diamonds often seen in playing cards or patterns.
• Kites: Some kites are designed in the shape of a rhombus.
• Windows: Certain types of window panes are rhombus-shaped.

Important Formulas:

• Area = 12×Diagonal1×Diagonal2\frac{1}{2} \times \text{Diagonal}_1 \times \text{Diagonal}_221​×Diagonal1​×Diagonal2​.
• Perimeter = 4 × Side.
• Diagonal Lengths: The diagonals are unequal, but they intersect at right angles.