What is a Trapezoid?

Trapezoid Definition

• A trapezoid is a quadrilateral with four sides
• Two definitions among mathematicians:
  • Exclusive definition: a quadrilateral with exactly one set of parallel sides
  • Inclusive definition: a quadrilateral with at least one pair of parallel sides

Trapezium Definition

• In Great Britain, the term trapezium means a quadrilateral with one set of parallel lines
• In the United States, the term means a quadrilateral with no pairs of parallel sides
• Derived from the Greek word trapezion, meaning a little table

Is a Square a Trapezoid?

• Exclusive definition separates trapezoids from parallelograms
• Inclusive definition includes parallelograms since they have two pairs of opposite sides parallel
• Both definitions are acceptable, with the inclusive definition favored in higher-level mathematics

Hierarchy of Quadrilaterals

• Quadrilaterals can be subdivided into parallelograms, kites, and trapezoids
• Parallelograms can be divided into rhombus and rectangle
• A square is a rectangle and a rhombus

Trapezoid Shapes

• Trapezoids come in various shapes depending on the lengths of the sides and the measure of the angles
• Examples of trapezoidal shapes are shown in the diagram

Real-Life Examples of Trapezoids

• Trapezoids are commonly used in engineering to design buildings and other structures
• Examples of famous architectural structures based on trapezoids include the Flatiron Building in New York, Diagonal Zero Zero in Barcelona, and the Gooderham Building in Ontario

Properties of a Trapezoid

• A trapezoid has two parallel sides called bases, two non-parallel sides called legs, and a line perpendicular to the bases called the height
• The sum of the angles of a trapezoid is 360 degrees
• The bases are parallel and never intersect
• If the legs are parallel, the quadrilateral is a parallelogram

Area of a Trapezoid

• The formula for the area of a trapezoid is 1/2h(b1+b2)
• Method 1: Use the formula
• Method 2: Decompose the figure into two triangles and a rectangle and add their areas

Perimeter of a Trapezoid

• The perimeter of a trapezoid is the sum of the lengths of the sides
• Example: P = 8 + 9 + 13 + 15 = 45 cm

Types of Trapezoids

• Right trapezoids: height is perpendicular to the bases, and one leg is also the height
• Isosceles trapezoids: legs are congruent, base angles are equal, and diagonals are equal
• Scalene trapezoids: no equal sides