Trapezoid

From WikiMD.com - Food, Medicine & Wellness Encyclopedia

Trapezoid[edit | edit source]

A trapezoid is a quadrilateral with at least one pair of parallel sides. In the context of geometry, trapezoids are a fundamental shape studied for their unique properties and applications in various fields such as architecture, engineering, and mathematics.

Diagram of a trapezoid

Definition and Properties[edit | edit source]

In Euclidean geometry, a trapezoid is defined as a four-sided figure, or quadrilateral, with at least one pair of parallel sides. These parallel sides are referred to as the "bases" of the trapezoid, while the non-parallel sides are called the "legs." The height of a trapezoid is the perpendicular distance between the bases.

The area of a trapezoid can be calculated using the formula:

\( A = \frac{1}{2} \times (b_1 + b_2) \times h \)

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides, and \( h \) is the height.

Types of Trapezoids[edit | edit source]

Trapezoids can be classified into several types based on their properties:

  • Isosceles Trapezoid: A trapezoid where the non-parallel sides (legs) are of equal length. This type of trapezoid has symmetrical properties and equal angles adjacent to each base.
  • Right Trapezoid: A trapezoid with one of the legs perpendicular to the bases, forming right angles.

Historical Context[edit | edit source]

File:Trapezium and Trapezoid, Hutton s mistake in 1795.png
Historical depiction of trapezoid terminology

The terminology surrounding trapezoids has varied historically and geographically. In British English, the term "trapezium" is often used to describe what is known as a trapezoid in American English, and vice versa. This discrepancy has led to some confusion in mathematical literature.

Comparison with Other Quadrilaterals[edit | edit source]

Comparison with a rhombus

Trapezoids are often compared to other quadrilaterals such as parallelograms, rhombuses, and rectangles. Unlike parallelograms, trapezoids have only one pair of parallel sides. A rhombus, on the other hand, has all sides of equal length, which is not a requirement for trapezoids.

Comparison with a rhomboid

Applications[edit | edit source]

Trapezoids are used in various practical applications, including the design of trapezoidal rule for numerical integration, architectural designs, and in the construction of trapezoidal threads in mechanical engineering.

Related Pages[edit | edit source]

Another trapezoid example

See Also[edit | edit source]

Trapezoid with labeled angles

Notes[edit | edit source]

The distinction between trapezoid and trapezium is important in understanding the geometric properties and applications of these shapes. The use of these terms can vary, so it is essential to clarify the context in which they are used.

Trapezium in British English
WikiMD
Navigation: Wellness - Encyclopedia - Health topics - Disease Index‏‎ - Drugs - World Directory - Gray's Anatomy - Keto diet - Recipes

Search WikiMD

Ad.Tired of being Overweight? Try W8MD's physician weight loss program.
Semaglutide (Ozempic / Wegovy and Tirzepatide (Mounjaro / Zepbound) available.
Advertise on WikiMD

WikiMD's Wellness Encyclopedia

Let Food Be Thy Medicine
Medicine Thy Food - Hippocrates

Medical Disclaimer: WikiMD is not a substitute for professional medical advice. The information on WikiMD is provided as an information resource only, may be incorrect, outdated or misleading, and is not to be used or relied on for any diagnostic or treatment purposes. Please consult your health care provider before making any healthcare decisions or for guidance about a specific medical condition. WikiMD expressly disclaims responsibility, and shall have no liability, for any damages, loss, injury, or liability whatsoever suffered as a result of your reliance on the information contained in this site. By visiting this site you agree to the foregoing terms and conditions, which may from time to time be changed or supplemented by WikiMD. If you do not agree to the foregoing terms and conditions, you should not enter or use this site. See full disclaimer.
Credits:Most images are courtesy of Wikimedia commons, and templates, categories Wikipedia, licensed under CC BY SA or similar.

Contributors: Prab R. Tumpati, MD