Question

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

Explanation:

Step1: Find area of large rectangle

The large rectangle has length \(l = 17\) cm and width \(w=8\) cm. The area formula for a rectangle is \(A = l\times w\). So the area of the large rectangle \(A_{1}=17\times8 = 136\) \(cm^{2}\).

Step2: Find area of small rectangle

The small rectangle has length \(l'= 8\) cm and width \(w' = 3\) cm. Using the area formula \(A = l\times w\), the area of the small rectangle \(A_{2}=8\times3=24\) \(cm^{2}\).

Step3: Calculate shaded - area

The shaded - area \(A\) is the area of the large rectangle minus the area of the small rectangle. So \(A=A_{1}-A_{2}=136 - 24=112\) \(cm^{2}\).

Answer:

\(112\) \(cm^{2}\)