Question

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

Explanation:

Answer:

First, find the dimensions of the outer rectangle. The length of the outer rectangle is \(6x + 2x=8x\) (since there are two \(x\) segments on the top and bottom), and the width is \(9x + 2x = 11x\) (since there are two \(x\) segments on the left and right). The area of the outer rectangle is \(length\times width=8x\times11x = 88x^{2}\).

The area of the inner (unshaded) rectangle is \(6x\times9x=54x^{2}\).

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

So the answer is \(34x^{2}\), which corresponds to the option B. 34x² (assuming the options are labeled A, B, C, D with B being 34x²)