Question

what is the area of this figure? 2 ft 8 ft 4 ft 16 ft 6 ft 3 ft 2 ft 9 ft square feet

Explanation:

Step1: Divide the figure into three rectangles

We can split the L - shaped figure into three rectangles. Let's define the three rectangles:

• Rectangle 1: The bottom - most rectangle with length \(l_1 = 9\) ft and height \(h_1=2\) ft.
• Rectangle 2: The middle rectangle. Its length \(l_2=9 - 3=6\) ft (since the bottom rectangle has a length of 9 ft and the part not included in the middle rectangle is 3 ft) and height \(h_2 = 6\) ft.
• Rectangle 3: The top - most rectangle. Its length \(l_3 = 2\) ft and height \(h_3=16-(2 + 6)=8\) ft (the total height is 16 ft, and we subtract the heights of the bottom two rectangles which are 2 ft and 6 ft).

Step2: Calculate the area of each rectangle

The area of a rectangle is given by the formula \(A = l\times h\).

• Area of Rectangle 1 (\(A_1\)):

\(A_1=l_1\times h_1=9\times2 = 18\) square feet.

• Area of Rectangle 2 (\(A_2\)):

\(A_2=l_2\times h_2 = 6\times6=36\) square feet.

• Area of Rectangle 3 (\(A_3\)):

\(A_3=l_3\times h_3=2\times8 = 16\) square feet.

Step3: Sum up the areas of the three rectangles

The total area \(A\) of the figure is the sum of the areas of the three rectangles.
\(A=A_1 + A_2+A_3\)
\(A = 18+36 + 16\)
First, \(18+36=54\), then \(54 + 16=70\).

Answer:

70