Question

the figure shows two rectangles. which expression represents the area of the shaded region? 16x² 34x² 54x² 88x²

Explanation:

Step1: Find the dimensions of the outer rectangle

The length of the outer rectangle: The inner length is \(6x\), and there are two \(x\) regions (top and bottom), so the outer length is \(6x + x + x = 8x\).
The width of the outer rectangle: The inner width is \(9x\), and there are two \(x\) regions (left and right), so the outer width is \(9x + x + x = 11x\).
The area of the outer rectangle is \(length\times width = 8x\times11x = 88x^{2}\).

Step2: Find the area of the inner rectangle

The inner rectangle has length \(6x\) and width \(9x\), so its area is \(6x\times9x = 54x^{2}\).

Step3: Find the area of the shaded region

The shaded region's area is the outer rectangle's area minus the inner rectangle's area: \(88x^{2}-54x^{2}=34x^{2}\).

Answer:

\(34x^{2}\) (corresponding to the option with \(34x^{2}\))