the figure shows two rectangles. which expression represents the area of the shaded region? 16x² 34x² 54x²…

Explanation:

Step1: Find outer - rectangle area

The length of the outer - rectangle is $9x + x+x=11x$ and the width is $6x + x+x = 8x$. The area of a rectangle is $A = l\times w$, so the area of the outer - rectangle $A_{outer}=11x\times8x = 88x^{2}$.

Step2: Find inner - rectangle area

The length of the inner - rectangle is $9x$ and the width is $6x$. The area of the inner - rectangle $A_{inner}=9x\times6x=54x^{2}$.

Step3: Find shaded - region area

The area of the shaded region $A = A_{outer}-A_{inner}$. So $A = 88x^{2}-54x^{2}=34x^{2}$.

Answer:

$34x^{2}$