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 formula for the area of a rectangle is \(A = l\times w\). For the larger rectangle, \(l = 12\space mm\) and \(w=7\space mm\). So, \(A_{1}=12\times7 = 84\space mm^{2}\)

Step2: Calculate the area of the smaller rectangle

For the smaller rectangle, \(l = 6\space mm\) and \(w = 3\space mm\). Using the area formula \(A = l\times w\), we get \(A_{2}=6\times3=18\space mm^{2}\)

Step3: Find the area of the shaded region

The area of the shaded region \(A\) is the area of the larger rectangle minus the area of the smaller rectangle. So, \(A=A_{1}-A_{2}\)
Substitute \(A_{1}=84\) and \(A_{2} = 18\) into the formula: \(A=84 - 18=66\space mm^{2}\)

Answer:

\(66\space mm^{2}\)