Questions and Answers
What is the main difference between the exclusive and inclusive definitions of a trapezoid?
What is the term used in Great Britain for a quadrilateral with one set of parallel lines?
Is a square a trapezoid according to the inclusive definition?
What is the origin of the term 'trapezium'?
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Why is the inclusive definition favored in higher-level mathematics?
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What is the main reason trapezoids are used in engineering to design buildings?
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What is the formula to calculate the area of a trapezoid?
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What is a characteristic of a right trapezoid?
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What is the perimeter of a trapezoid?
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What is a type of trapezoid that has all sides of equal length?
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What is a characteristic of an isosceles trapezoid?
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What is true about the diagonals of an isosceles trapezoid?
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What type of trapezoid has no equal sides?
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What can a right trapezoid be easily decomposed into?
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What is a characteristic of the legs of an isosceles trapezoid?
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Study Notes
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
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Description
Learn about the different definitions of a trapezoid, a quadrilateral shape with parallel sides, and its variations in Great Britain and the United States.
