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Rhombus: Types, Properties and Formulas

What is a Rhombus?

A rhombus is a special kind of polygon, specifically a quadrilateral, characterized by four equal-length sides, with opposite sides running parallel to each other. Often called a diamond or a slanting square, the rhombus stands out in geometry for its symmetrical properties and its distinctive look.

Types of Rhombus

While the rhombus is a unique quadrilateral on its own, it relates closely to other shapes:

  • Square: A rhombus with all right angles.
  • Rectangle: Similar to a rhombus but with unequal adjacent sides and all right angles. This classification helps distinguish a rhombus from other parallelograms.

Properties of a Rhombus

The rhombus is known for several key properties:

  • Four sides of equal length.
  • Opposite sides are parallel.
  • Opposite angles are equal.
  • Diagonals bisect each other at right angles, making them perpendicular.
  • Diagonals bisect the angles from which they are drawn.

Formulas of Rhombus

Understanding a rhombus involves knowing how to calculate its area and perimeter:

  • Area: The area can be calculated using the formula where you multiply the lengths of the diagonals together and then divide by 2.
  • Perimeter: To find the perimeter, multiply the length of one side by 4.

Example

Imagine a rhombus with each side measuring 5 cm and diagonals that are 8 cm and 6 cm long:

  • Area: (8 cm * 6 cm) / 2 = 24 cm²
  • Perimeter: 4 * 5 cm = 20 cm

FAQs about Rhombus

Q: How is a rhombus different from a square?
A: Both have four sides of equal length, but a square requires all right angles, which a rhombus does not necessarily have.

Q: Can a rhombus have right angles?
A: Yes, if a rhombus has right angles, it is also a square.

Q: Is every rhombus considered a diamond?
A: In everyday language, rhombuses are often referred to as diamonds, especially when discussing shapes and designs. They are essentially the same in mathematical terms.

Q: Why are the diagonals of a rhombus perpendicular to each other?
A: The diagonals in a rhombus intersect at right angles due to the shape’s symmetrical nature.

Mathematics

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