Question

How many square feet of outdoor carpet are needed for this hole

Answer 1

The area of a rectangle is:

`Ar=l\cdot h`

Where:

Ar = area of the rectangle

l = lenght

w = width

And the area of a triangle is:

`At=(1)/(2)\cdot b\cdot h`

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.

`\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}`

Step 02: Calculate A2.

Figure2 is a rectangle with sides 2 and 3 ft.

`\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}`

Step 03: Calculate A3.

Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.

`\begin{gathered} A3=(4\cdot3)/(2) \\ A3=(12)/(2) \\ A3=6ft^2 \end{gathered}`

Step 04: Calculate A4.

Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.

`\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}`

Step 05: Calculate A5.

Figure 5 is a rectangle with sides 2 and 5 ft.

`\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}`

Step 06: Find the area of the figure.

A = A1 - A2 + A3 + A4 + A5.

`\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}`

Answer: 48 ft² is needed for this hole.