Given that,
The height of a trapezoid is (2x + 9).
The bases can be expressed as (3x - 7) and (x + 5).
To find,
An expression represent the area of the trapezoid.
Solution,
The formula for the area of trapezoid is given by :
[tex]A=\dfrac{1}{2}(\text{sum of bases})\times \text{height}[/tex]
Put all the values,
[tex]A=\dfrac{1}{2}(3x-7+x+5)\times (2x+9)\\\\=\dfrac{1}{2}(4x-2)\times (2x+9)\\\\=(2x-1)(2x+9)\\\\A=2x(2x)+9(2x)+(-1)(2x)+(-1)(9)\\\\=4x^2+18x-2x-9\\\\=4x^2+16x-9[/tex]
So, the area of the trapezoid will be [tex](4x^2+16x-9)\ \text{units}^2[/tex]
