Question

find the area of the figure. (sides meet at right angles.)

Explanation:

Step1: Divide the figure into two rectangles

The figure can be divided into a lower rectangle with length \(7\) ft and width \((6 - 2)=4\) ft, and an upper rectangle with length \(3\) ft and width \(2\) ft.

Step2: Calculate the area of the lower rectangle

The area formula for a rectangle is \(A = l\times w\). For the lower rectangle, \(l = 7\) ft and \(w=(6 - 2)=4\) ft. So \(A_{1}=7\times4 = 28\) \(ft^{2}\).

Step3: Calculate the area of the upper rectangle

For the upper rectangle, \(l = 3\) ft and \(w = 2\) ft. Using the area formula \(A = l\times w\), we get \(A_{2}=3\times2=6\) \(ft^{2}\).

Step4: Sum the areas of the two rectangles

The total area \(A=A_{1}+A_{2}\). Substitute \(A_{1} = 28\) \(ft^{2}\) and \(A_{2}=6\) \(ft^{2}\) into the formula. So \(A=28 + 6=34\) \(ft^{2}\).

Answer:

\(34\)