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Determine the simplified expression for the area of the shaded region below

Determine the simplified expression for the area of the shaded region below-example-1

1 Answer

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Answer:

shaded area = 9x² +10x +4

Explanation:

The area of the shaded region is the difference between the areas of the overall rectangle and the unshaded one it contains. Each area is the product of length and width.

Rectangle areas

Overall rectangle

A = LW

A = (5x)(3x) = 15x² . . . . . using given dimensions

Unshaded interior rectangle

A = (3x +1)(2x -4) = 3x(2x -4) +1(2x -4) . . . . . using given dimensions

A = 6x² -12x +2x -4 = 6x² -10x -4

Difference of areas

The shaded area is the difference between the area of the overall rectangle and the area of the unshaded included rectangle.

shaded area = (15x²) -(6x² -10x -4)

shaded area = 9x² +10x +4

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