Area and Volume of Rectangles

The video tutorial explains how to determine the area of a rectangle using both factored and expanded forms. It begins by introducing the formula for the area of a rectangle as length times width. The tutorial then demonstrates how to expand the formula by distributing terms and combining like terms. Finally, it calculates the area using a specific value for X, showing that both the factored and expanded forms yield the same result.

What is the general formula for the area of a rectangle?

• Length / Width

• Length - Width

• Length x Width

• Length + Width

For the given rectangle, what is the formula to determine its area?

• (2x + 3) - (x - 3)

• (2x + 3) + (x - 3)

• (2x + 3) x (x - 3)

• (2x + 3) / (x - 3)

What is the result of distributing 2x to both terms in the expression (2x + 3)(x - 3)?

• 2x^2 and -6x

• 2x^2 and 3x

• 2x^2 and -9

• 2x^2 and 6x

What is the result of distributing 3 to both terms in the expression (2x + 3)(x - 3)?

• 3x and -6x

• 3x and -9

• 3x and 9

• 3x and 3

What are the like terms in the expanded form of the area formula?

• 2x^2 and -9

• 2x^2 and 3x

• -6x and -9

• -6x and 3x

What is the simplified form of the area formula after combining like terms?

• 2x^2 + 3x - 9

• 2x^2 - 3x - 9

• 2x^2 + 6x - 9

• 2x^2 - 6x + 9

Using the expanded form, what is the area of the rectangle when x = 6?

• 54 square units

• 72 square units

• 45 square units

• 36 square units

Using the factored form, what is the area of the rectangle when x = 6?

• 54 square units

• 45 square units

• 36 square units

• 72 square units