Question

what is the area of this figure? (figure with labeled lengths: 2 ft, 2 ft, 2 ft, 3 ft, 2 ft, 6 ft, 2 ft, 4 ft, 8 ft, 15 ft)

Explanation:

Step1: Divide the figure into rectangles

Divide the figure into 4 rectangles.

Step2: Calculate the area of each rectangle

• For the bottom - left rectangle: length \(l_1 = 4\) ft, width \(w_1=2\) ft. Area \(A_1=l_1\times w_1 = 4\times2=8\) \(ft^2\).
• For the middle - left rectangle: length \(l_2 = 6\) ft, width \(w_2 = 2\) ft. Area \(A_2=l_2\times w_2=6\times2 = 12\) \(ft^2\).
• For the upper - left rectangle: length \(l_3=3\) ft, width \(w_3 = 2\) ft. Area \(A_3=l_3\times w_3=3\times2=6\) \(ft^2\).
• For the right - most rectangle: length \(l_4 = 15\) ft, width \(w_4=2\) ft. Area \(A_4=l_4\times w_4=15\times2 = 30\) \(ft^2\).
• There is also a large rectangle with length \(l_5=8\) ft and width \(w_5=(15-(4 + 6+3))=2\) ft. Area \(A_5=l_5\times w_5=8\times2=16\) \(ft^2\).

Step3: Sum up the areas of all rectangles

\(A=A_1 + A_2+A_3+A_4+A_5\)
\(A=8 + 12+6+30+16\)
\(A = 72\) \(ft^2\)

Answer:

The area of the figure is \(72\) square feet.