The area of a rectangle is:
[tex]Ar=l\cdot h[/tex]
Where:
Ar = area of the rectangle
l = lenght
w = width
And the area of a triangle is:
[tex]At=\frac{1}{2}\cdot b\cdot h[/tex]
Where:
At = area of the triangle
b = base
h = height
To solve this problem divide the figure into triangles and rectangles, according to the figure below.
And the square feed (A) needed will be:
A = A1 - A2 + A3 + A4 + A5
Step 01: Calculate A1.
Figure 1 is a rectangle with sides 5 and 6 ft.
[tex]\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}[/tex]
Step 02: Calculate A2.
Figure2 is a rectangle with sides 2 and 3 ft.
[tex]\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}[/tex]
Step 03: Calculate A3.
Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.
[tex]\begin{gathered} A3=\frac{4\cdot3}{2} \\ A3=\frac{12}{2} \\ A3=6ft^2 \end{gathered}[/tex]
Step 04: Calculate A4.
Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.
[tex]\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}[/tex]
Step 05: Calculate A5.
Figure 5 is a rectangle with sides 2 and 5 ft.
[tex]\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}[/tex]
Step 06: Find the area of the figure.
A = A1 - A2 + A3 + A4 + A5.
[tex]\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}[/tex]
Answer: 48 ft² is needed for this hole.
