The area of the trapezoid is the amount of space on it.
The area of the trapezoid is [tex]4x^2 - 5x +1[/tex]
The area of a shape is the amount of space the shape occupies
The given parameters are:
The area of a trapezoid is calculated as:
[tex]Area = \frac 12 \times (Base\ 1 + Base\ 2) \times Height[/tex]
So, we have:
[tex]Area = \frac 12 \times (5x - 4 + 3x + 2) \times (x -1)[/tex]
Collect like terms
[tex]Area = \frac 12 \times (5x + 3x - 4 + 2) \times (x -1)[/tex]
Evaluate the like terms
[tex]Area = \frac 12 \times (8x - 2 ) \times (x -1)[/tex]
Evaluate the product
[tex]Area = (4x - 1) \times (x -1)[/tex]
Open the brackets
[tex]Area = 4x^2 - 4x -x +1[/tex]
Evaluate the like terms
[tex]Area = 4x^2 - 5x +1[/tex]
Hence, the area of the trapezoid is [tex]4x^2 - 5x +1[/tex]
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