Question

what is the area of this figure? 13 ft 4 ft 6 ft 7 ft 2 ft 6 ft square feet submit work it out not feeling ready yet? these ca area of rectangles and squares (100)

Explanation:

Step1: Split the figure into two rectangles

We can split the given figure into two rectangles. The first rectangle has dimensions \(13\) ft (length) and \(4\) ft (height), and the second rectangle has dimensions \(6\) ft (length) and \(2\) ft (height) (since \(6 - 4=2\) ft, and the length of the second rectangle is \(13 - 7 = 6\) ft? Wait, no, let's re - examine. Alternatively, we can consider the large rectangle without the notch and then subtract the area of the notch, or split it into two rectangles. Let's use the split method:

First rectangle: length \(13\) ft, height \(4\) ft. Area of first rectangle \(A_1=13\times4\)

Second rectangle: The remaining part. The height of the second part is \(6 - 4=2\) ft, and the length is \(13 - 7 = 6\) ft? Wait, no, looking at the figure, the bottom part that is extended: the horizontal length for the lower rectangle is \(6\) ft (given), and the vertical length is \(2\) ft (since \(6 - 4 = 2\)). Wait, another way: The total figure can be seen as a rectangle of length \(13\) ft and height \(6\) ft minus a rectangle of length \(7\) ft and height \(2\) ft.

Let's verify: The large rectangle (if we consider the outer dimensions) would be \(13\) ft (length) and \(6\) ft (height), area \(A_{large}=13\times6\). The notch (the missing part) is a rectangle with length \(7\) ft and height \(2\) ft, area \(A_{notch}=7\times2\). Then the area of the figure \(A = A_{large}-A_{notch}\)

Step2: Calculate the area of the large rectangle

The area of a rectangle is given by the formula \(A = l\times w\), where \(l\) is the length and \(w\) is the width. For the large rectangle with \(l = 13\) ft and \(w = 6\) ft, \(A_{large}=13\times6=78\) square feet.

Step3: Calculate the area of the notch

The notch is a rectangle with \(l = 7\) ft and \(w = 2\) ft. Using the area formula for a rectangle, \(A_{notch}=7\times2 = 14\) square feet.

Step4: Calculate the area of the figure

Subtract the area of the notch from the area of the large rectangle: \(A=A_{large}-A_{notch}=78 - 14=64\) square feet.

Wait, let's check with the split method. First rectangle: length \(13\) ft, height \(4\) ft, \(A_1 = 13\times4=52\) square feet. Second rectangle: length \(6\) ft (since \(13 - 7 = 6\)), height \(2\) ft (since \(6 - 4 = 2\)), \(A_2=6\times2 = 12\) square feet. Then total area \(A=A_1 + A_2=52+12 = 64\) square feet.

Answer:

\(64\)