Podcast
Questions and Answers
What is the area of the rectangle in the trapezoid?
What is the area of the rectangle in the trapezoid?
30
What is the area of one triangle in the trapezoid?
What is the area of one triangle in the trapezoid?
5
What is the area of the other triangle in the trapezoid?
What is the area of the other triangle in the trapezoid?
5
What is the perimeter of the trapezoid?
What is the perimeter of the trapezoid?
Signup and view all the answers
What is the exclusive definition of a trapezoid?
What is the exclusive definition of a trapezoid?
Signup and view all the answers
What is the inclusive definition of a trapezoid?
What is the inclusive definition of a trapezoid?
Signup and view all the answers
Why is the inclusive definition favored in higher level mathematics?
Why is the inclusive definition favored in higher level mathematics?
Signup and view all the answers
What are the properties of an isosceles trapezoid?
What are the properties of an isosceles trapezoid?
Signup and view all the answers
Study Notes
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on trapezoids with this quiz! Learn about the exclusive and inclusive definitions, understand the distinguishing features, and explore the relationship with parallelograms.
