First, we need to find the sides of the triangle.
The base of the triangles is 8ft - 5ft = 3ft.
The height for the triangle is 7ft - 4ft = 3ft
Now, we need to find the area of the triangle:
[tex]A_t=\frac{base\cdot height}{2}[/tex]
Replacing the values:
[tex]A_t=\frac{3ft\cdot3ft}{2}[/tex]
Then
[tex]A_t=4.5ft^2^{}[/tex]
Now, we need to find the area for the rectangle:
Area for a rectangle = Length * Width
In this case:
Length = 8ft
Width = 7ft
Therefore:
[tex]A_r=8ft\cdot7ft[/tex]
Then
[tex]A_r=56[/tex]
Finally, to find the area of the shaded region we need to subtract the triangle area from the rectangle area:
[tex]A=A_r-A_t[/tex]
Therefore:
[tex]A=56ft^2-4.5ft^2[/tex][tex]A=51.5ft^2[/tex]
Hence, the area for the shaded region is 51.5 ft².
