Exploring the Area of a Trapezoid Formula

The video tutorial demonstrates how to prove that the area of a trapezoid is the average of its bases multiplied by its height. The instructor begins by drawing a trapezoid and explaining its dimensions. The proof involves creating a copy of the trapezoid, flipping it, and forming a parallelogram. The area of the parallelogram is calculated using known formulas, and the result is used to derive the area of the trapezoid. The video concludes with a rearrangement of the formula to show the trapezoid's area as the average of the bases times the height.

What is the first step in proving the area formula for a trapezoid?

• Measuring the bases

• Creating a parallelogram

• Calculating the height

• Drawing the trapezoid

What geometric shape is formed by duplicating and flipping the trapezoid?

• Triangle

• Rectangle

• Circle

• Parallelogram

What assumption is made in the proof regarding the area of a parallelogram?

• It is twice the area of a trapezoid

• It is equal to the base times height

• It is less than the area of the trapezoid

• It depends on the angle between the bases

Which type of trapezoid was used in the video to demonstrate the proof?

• Isosceles trapezoid

• Right trapezoid

• Scalene trapezoid

• Equilateral trapezoid

How does duplicating and flipping the trapezoid help in proving the area formula?

• It simplifies the shape into a more complex figure

• It doubles the area of the trapezoid

• It creates a parallelogram, which is easier to calculate

• It helps in visualizing the trapezoid better

What is the height of the parallelogram formed in the proof?

• The length of the shorter base

• The length of the longer base

• The altitude of the trapezoid

• The sum of the bases

How is the base of the parallelogram determined in the proof?

• By dividing the height by two

• By subtracting the shorter base from the longer base

• By adding the lengths of the bases of the trapezoid

• By multiplying the heights

What is the significance of the height 'H' in the area calculation?

• It is used as the base in the parallelogram

• It represents the slanted side of the trapezoid

• It is the altitude used in the area calculation

• It is irrelevant to the area calculation

What operation is performed to find the area of one trapezoid from the parallelogram?

• Subtraction of heights

• Addition of base lengths

• Division by two

• Multiplication by two

What does the area formula of a trapezoid involve?

• The difference between the bases

• Multiplying the bases by two

• The average of the bases times the height

• The sum of all sides