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 of a rectangle is given by \(A = length\times width\). For the larger rectangle with length \(9\) yd and width \(8\) yd, the area \(A_{1}=9\times8 = 72\) square yards.

Step2: Calculate the area of the smaller rectangle

For the smaller rectangle with length \(3\) yd and width \(2\) yd, the area \(A_{2}=3\times2=6\) square yards.

Step3: Calculate 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 \(A_{1}=72\) and \(A_{2} = 6\) into the formula: \(A=72 - 6=66\) square yards.

Answer:

The area of the shaded region is \(66\) square yards.