## Intermediate Algebra (6th Edition)

$(x^2-7x) \text{ square units}$
The shaded region is a trapezoid with $h=(x-7), b_1=x,$ and $b_2=3x.$ Using $A=\dfrac{h(b_1+b_2)}{2}$ or the formula for the area of a trapezoid, then \begin{array}{l}\require{cancel} A=\dfrac{(x-7)(x+3x)}{2} \\ A=\dfrac{(x-7)(4x)}{2} \\ A=\dfrac{(x-7)(\cancel2^2x)}{\cancel2} \\ A=x(x-7) .\end{array} Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} A=x(x)+x(-7) \\ A=x^2-7x .\end{array} Hence, the area is $(x^2-7x) \text{ square units} .$