Trapezoid Quiz

Trapezoid Definitions

• A trapezoid is a quadrilateral with two different definitions: exclusive and inclusive.
• Exclusive definition: a quadrilateral with exactly one set of parallel sides.
• Inclusive definition: a quadrilateral with at least one pair of parallel sides.

Quadrilateral Hierarchy

• The hierarchy of quadrilaterals using the exclusive definition includes:
  • Parallelograms
  • Kites
  • Trapezoids
• Parallelograms can be divided into:
  • Rhombus
  • Rectangle
• A square is a rectangle and a rhombus.

Trapezoid vs. Trapezium

• The term "trapezium" has two definitions:
  • In Great Britain, it means a quadrilateral with one set of parallel lines.
  • In the United States, it means a quadrilateral with no pairs of parallel sides.

Trapezoid Shapes and Properties

• Trapezoids come in various shapes depending on the lengths of the sides and the measure of the angles.
• Trapezoids are commonly used in engineering to design buildings and structures.
• Famous architectural structures based on trapezoids include:
  • Diagonal Zero Zero (Barcelona, Spain)
  • The Gooderham Building (Ontario, Canada)
  • The Flatiron Building (New York, NY)

Attributes of a Trapezoid

• A trapezoid has:
  • Two parallel sides called bases
  • Two non-parallel sides called legs
  • A line perpendicular to the bases called the height (or altitude)
• The sum of the angles of a trapezoid is 360 degrees.
• The bases of a trapezoid never intersect.

Types of Trapezoids

• Right Trapezoids:
  • Have a 90-degree angle with the bases
  • Can be easily decomposed into a rectangle and a triangle
• Isosceles Trapezoids:
  • Have legs that are congruent
  • Base angles are congruent
  • Diagonals are congruent
• Scalene Trapezoids:
  • Have no equal sides

Area of a Trapezoid

• The formula for the area of a trapezoid is: 1/2h(b1+b2)
• Example: a trapezoid with a height of 5 and bases of 6 and 10 has an area of 40.

Perimeter of a Trapezoid

• The perimeter of a trapezoid is the sum of the lengths of its sides.
• Example: a trapezoid with sides of 8, 9, 13, and 15 has a perimeter of 45 cm.