Understanding Area Decomposition

The video tutorial explains how to find and simplify the expression for the area of a blue shaded region by decomposing it into smaller rectangles. It demonstrates two methods of decomposition, calculates the areas of the rectangles, and simplifies the resulting expression. The tutorial concludes by verifying the calculations and ensuring the expression is correct.

What is the initial strategy used to find the area of the blue shaded region?

• Using trigonometric identities

• Applying the formula for the area of a circle

• Decomposing the area into smaller rectangles

• Using the Pythagorean theorem

Tags

CCSS.2.MD.A.3

How is the length of the unknown side of the first rectangle determined?

• By using the area formula

• By adding the known length to the total length

• By subtracting the known length from the total length

• By measuring it directly

Tags

CCSS.HSA.APR.D.6

What is the expression for the area of the first rectangle (a sub 1)?

• x * (x - 1)

• 6 * x

• x + 6

• x^2 + 5x

What is the simplified expression for the total area of the blue shaded region?

• 6x + x

• x^2 + 6x

• x^2 + 5x

• x^2 + 6

Tags

CCSS.4.MD.A.2

In the alternative decomposition method, what is the length of the short side of the small rectangle?

• x - 1 units

• x units

• 6 units

• 1 unit

Tags

CCSS.HSA-REI.B.4B

What is the area of the small rectangle in the alternative decomposition method?

• x + 6 square units

• x * (x - 1) square units

• x^2 square units

• 6 square units

Tags

CCSS.HSA-REI.B.4B

What is the expression for the area of the large rectangle in the alternative decomposition method?

• x + 6 * (x - 1)

• 6 * x

• x + 6

• x * (x - 1)

What is the result of multiplying and simplifying the expression for the total area in the verification step?

• 6x + x

• x^2 + 5x

• x^2 + 6

• x^2 + 6x

Tags

CCSS.RI.7.7

CCSS.RI.8.7

CCSS.RL.7.7

CCSS.RL.8.7

CCSS.RL.9-10.7

What is the purpose of the verification step in the video?

• To introduce a new method

• To confirm the initial result

• To calculate a new area

• To find a different solution

What is the final expression for the total area of the blue shaded region?

• x^2 + 5x

• x^2 + 6x

• 6x + x

• x^2 + 6