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23 December, 05:36

Write an expression for the area of the shaded region in its simplest form. Show all of your steps.

The whole shaded area is a rectangle that is:

x+10 by 2x+5

Then there is a plain white square inside the larger rectangle that is:

x+1 by x+1

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  1. 23 December, 05:55
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    The area of the shaded region is going to be the area of the rectangle minus the area of the square.

    Area of a rectangle is L * W.

    A = L * W

    A = (x + 10) (2x + 5)

    A = x (2x + 5) + 10 (2x + 5)

    A = 2x^2 + 5x + 20x + 50

    A = 2x^2 + 25x + 50 ... this is the area of the rectangle

    area of a square is : A = a^2 ... where a is one side

    A = (x + 1) ^2

    A = (x + 1) (x + 1)

    A = x (x + 1) + 1 (x + 1)

    A = x^2 + x + x + 1

    A = x^2 + 2x + 1

    now we subtract the area of the square from the area of the rectangle to get the area of the shaded region.

    2x^2 + 25x + 50 - (x^2 + 2x + 1) =

    2x^2 + 25x + 50 - x^2 - 2x - 1 =

    x^2 + 23x + 49 < = = the area of the shaded region
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