Solution:
Given:
[tex]\begin{gathered} Area\text{ of mat before it is cut}=M(x)=1.5x^2+13x+20 \\ Area\text{ of mat that was cut out from the middle}=N(x)=x^2+7x \end{gathered}[/tex]
The area of the cut mat is the part of the mat left after the middle one is cut out.
The area of the cut mat is the shaded portion.
Hence,
[tex]\begin{gathered} A(x)=M(x)-N(x) \\ A(x)=1.5x^2+13x+20-(x^2+7x) \\ A(x)=1.5x^2-x^2+13x-7x+20 \\ A(x)=0.5x^2+6x+20 \end{gathered}[/tex]
Therefore, the correct answer is OPTION A.
