Question

what is the area of this figure?
9 in
4 in
5 in
9 in
5 in
14 in
square inches

Explanation:

Step1: Divide the figure into two rectangles

We can split the L - shaped figure into a smaller rectangle and a larger rectangle. The first rectangle has dimensions \(5\) in (height) and \(14\) in (width)? Wait, no. Wait, let's look again. Alternatively, we can take the rectangle with length \(9\) in and width \(9\) in? No, better way: the bottom rectangle has height \(5\) in and width \(14\) in, and the top rectangle has height \(4\) in and width \(9\) in (since \(14 - 5=9\)).

Step2: Calculate the area of the bottom rectangle

The area of a rectangle is given by \(A = l\times w\), where \(l\) is length and \(w\) is width. For the bottom rectangle, \(l = 14\) in and \(w = 5\) in. So \(A_1=14\times5 = 70\) square inches.

Step3: Calculate the area of the top rectangle

The top rectangle has length \(9\) in (since \(14 - 5 = 9\)) and width \(4\) in (since \(9 - 5=4\)). So \(A_2=9\times4=36\) square inches.

Step4: Sum the areas of the two rectangles

The total area \(A = A_1+A_2=70 + 36=106\) square inches.

Alternatively, another way: The large rectangle (if we consider the outer rectangle) would be \(14\times9\), but we subtract the area of the missing rectangle. The missing rectangle has dimensions \(5\) in (length) and \(4\) in (width). So \(A=14\times9-5\times4=126 - 20 = 106\) square inches.

Answer:

\(106\)