Question

a rectangular region is removed from another rectangular region to create the shaded region shown below. find the area of the shaded region.

Explanation:

Step1: Calculate the area of the larger rectangle

The area formula for a rectangle is \(A = l\times w\). For the larger rectangle with \(l = 12\) cm and \(w=9\) cm, \(A_{1}=12\times9 = 108\) \(cm^{2}\).

Step2: Calculate the area of the smaller rectangle

For the smaller rectangle with \(l = 8\) cm and \(w = 5\) cm, using the formula \(A=l\times w\), \(A_{2}=8\times5=40\) \(cm^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A = A_{1}-A_{2}\). Substitute \(A_{1}=108\) \(cm^{2}\) and \(A_{2} = 40\) \(cm^{2}\) into the formula: \(A=108 - 40=68\) \(cm^{2}\).

Answer:

\(68\)