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 large rectangle

The formula for the area of a rectangle is \(A = l\times w\). For the large rectangle with length \(l = 16\) yd and width \(w=9\) yd, the area \(A_{1}=16\times9 = 144\) \(yd^{2}\).

Step2: Calculate the area of the small rectangle

For the small rectangle with length \(l = 7\) yd and width \(w = 5\) yd, using the area formula \(A=l\times w\), the area \(A_{2}=7\times5=35\) \(yd^{2}\).

Step3: Calculate the area of the shaded region

The area of the shaded region \(A\) is the area of the large rectangle minus the area of the small rectangle. So \(A=A_{1}-A_{2}\). Substitute \(A_{1} = 144\) \(yd^{2}\) and \(A_{2}=35\) \(yd^{2}\) into the formula: \(A=144 - 35=109\) \(yd^{2}\).

Answer:

\(109\)