Question

find the area of this irregular shape.
a = ? ft²
find the area of rectangle 1.

Explanation:

Step1: Calculate the area of the large rectangle

The formula for the area of a rectangle is \(A = length\times width\). The large rectangle has a length of \(8\) ft and a width of \(3\) ft. So, \(A_1=8\times3 = 24\) \(ft^2\).

Step2: Calculate the area of the two middle - sized rectangles

Each of the two middle - sized rectangles has a length of \(3\) ft and a width of \(2\) ft. The area of one such rectangle is \(A_{middle}=3\times2=6\) \(ft^2\). For two rectangles, \(A_2 = 2\times6=12\) \(ft^2\).

Step3: Calculate the area of the top - left square

Assume the side length of the square (rectangle 1) is \(2\) ft (by visual inspection of the figure's proportion, since the vertical segments \(2\) ft and \(3\) ft are given and the square's side matches the \(2\) - ft vertical segment in the non - large rectangle part). The area of a square is \(A = s\times s\), so \(A_3=2\times2 = 4\) \(ft^2\).

Step4: Calculate the total area

The total area \(A\) of the irregular shape is the sum of the areas of the three parts. \(A=A_1 + A_2+A_3\). Substitute \(A_1 = 24\), \(A_2 = 12\), and \(A_3 = 4\) into the formula: \(A=24 + 12+4=40\) \(ft^2\).

Answer:

\(40\)