Definition

1. Noun:
   • A quadrilateral with exactly one pair of parallel sides: In geometry, a trapezoid is a four-sided flat shape (quadrilateral) where one pair of opposite sides is parallel. This is the primary definition in many regions, including the United States and Canada.
   • A quadrilateral with at least one pair of parallel sides: In some regions (e.g., the UK), a trapezoid is defined as a quadrilateral with at least one pair of parallel sides, which can include shapes like parallelograms.
   • A small bone in the wrist: In anatomy, the trapezoid is one of the eight carpal bones in the wrist, located between the trapezium and the capitate bones.

Usage Examples

• Noun (Geometry):
  • The area of a trapezoid is calculated by multiplying the average of the parallel sides by the height.
  • She drew a perfect trapezoid on the whiteboard, labeling the two parallel sides 'a' and 'b'.
• Noun (Anatomy):
  • A fracture of the trapezoid bone can cause significant pain and limit wrist mobility.
  • The surgeon carefully examined the position of the trapezoid in the X-ray.

Advanced Usage

• "Isosceles trapezoid": A trapezoid where the non-parallel sides (legs) are equal in length, and the base angles are equal.
  • An isosceles trapezoid has a line of symmetry through the midpoints of its parallel sides.
• "Right trapezoid": A trapezoid that has two adjacent right angles.
  • A right trapezoid is often easier to work with when calculating area.

Variants and Related Words

• Trapezoidal (adj): Having the shape of a trapezoid.
  • The building featured a distinctive trapezoidal roof.
• Trapezium (n): In geometry, this term's meaning is often the opposite of 'trapezoid' depending on the region. In the US, a trapezium is a quadrilateral with no parallel sides. In anatomy, it is a different carpal bone adjacent to the trapezoid.
  • The terms 'trapezoid' and 'trapezium' have swapped definitions in British and American English.

Synonyms

• Quadrilateral: A general term for any four-sided polygon.
• Irregular quadrilateral: Emphasizes that the sides are not all equal or parallel (for the common US definition).

Related Phrases

• "Properties of a trapezoid": Refers to its geometric characteristics, such as angles, side lengths, and area formulas.
  • We studied the properties of a trapezoid in today's geometry class.
• "Midsegment of a trapezoid": The segment connecting the midpoints of the non-parallel sides; it is parallel to the bases and its length is the average of the lengths of the bases.
  • The midsegment of a trapezoid is a useful tool for solving many problems.

Noun

1. the wrist bone between the trapezium and the capitate bones
2. a quadrilateral with two parallel sides