Understanding Area Between Rectangles

The video tutorial explains how to find the area between two rectangles by subtracting the area of a smaller rectangle from a larger one. It provides a step-by-step derivation of the expression for the shaded area and demonstrates the calculation when x equals four meters, resulting in an area of 126 square meters.

What is the initial strategy to find the area between two rectangles?

• Subtract the area of the smaller rectangle from the larger one.

• Add the areas of both rectangles.

• Divide the area of the larger rectangle by the smaller one.

• Multiply the areas of both rectangles.

How do you calculate the area of a rectangle?

• Length plus width

• Length minus width

• Length times width

• Length divided by width

What is the expression for the area of the large rectangle?

• (x + 8)(x + 2)

• (x + 7)(x + 2)

• (x + 12)(x + 8)

• (x + 12)(x + 7)

What is the expression for the area of the small rectangle?

• (x + 8)(x + 2)

• (x + 12)(x + 7)

• (x + 7)(x + 2)

• (x + 12)(x + 8)

What is the first step in simplifying the expression for the shaded area?

• Multiply the areas of both rectangles.

• Add the areas of both rectangles.

• Distribute and combine like terms.

• Divide the areas of both rectangles.

What is the expression for the area of the shaded region after simplification?

• x^2 + 8x + 12x

• x^2 - 9x + 14

• 11x + 82

• x^2 + 20x + 96

What operation is performed to find the difference between the two areas?

• Division

• Multiplication

• Subtraction

• Addition

What is the final step in solving for the area of the shaded region?

• Adding the areas of both rectangles

• Subtracting the areas of both rectangles

• Combining like terms

• Distributing a negative one

What is the next step after finding the expression for the shaded area?

• Divide the expression by x.

• Multiply the expression by 2.

• Add 10 to the expression.

• Substitute a specific value for x.

What is the area of the shaded region when x equals 4 meters?

• 44 square meters

• 126 square meters

• 82 square meters

• 96 square meters