The coordinates of the vertices of the floor plan are given in the image provided in the question.
Before we can calculate the area, we need to get the lengths of the sides. This we can do by subtracting the coordinates of consecutive vertices. Note that the vertices are in the form (x, y). The x-coordinates are for horizontal lengths, while the y-coordinates are for vertical lengths.
For instance, the length first vertical line to the extreme left of the image can be gotten by subtracting as shown below:
[tex]13-0=13ft[/tex]
and the base of the image can be gotten to be:
[tex]9-0=9ft[/tex]
The image of the shape of the floor plan with the floor lengths is shown below:
To find the area, we can divide the shape into manageable chunks. These are shown below:
Area of A
Using the formula to find the area of a rectangle given to be:
[tex]A=l\times b[/tex]
the area of A is calculated to be:
[tex]A_A=13\times5=65ft^2[/tex]
Area of B
Using the formula for the area of a rectangle as well, we have:
[tex]A_B=16\times4=64ft^2[/tex]
Area of C
This is calculated to be:
[tex]A_C=8\times5=40ft^2[/tex]
Combined Area of the Floor
This is calculated as the sum of all the areas. This is gotten to be:
[tex]\begin{gathered} A=A_A+A_B+A_C \\ A=65+64+40=169ft^2 \end{gathered}[/tex]
The area of the floor is 169 square feet.
