we are asked to determine the surface area of the figure. To do that we need to find the areas of each face and add them together. The front face is a trapezoid, and its area is:
[tex]A_{tz}=\frac{b+B}{2}h[/tex]
Where "b" is the upper base, "B" is the lower base and "h" is the height. Replacing the values:
[tex]A_{tz}=\frac{9ft+4ft}{2}\times4.3ft[/tex]
Solving the operations:
[tex]A_{tz}=28ft^2[/tex]
the upper face is a rectangle, its area is the product of its side:
[tex]A_{uf}=(10ft)(9ft)=90ft^2[/tex]
The area of the lower face is also a rectangle, therefore its area is:
[tex]A_{lf}=(4ft)(10ft)=40ft^2[/tex]
The side face is also a rectangle, and its area is:
[tex]A_{sf}=(5ft)(10ft)=50ft^2[/tex]
Now we add the areas having into account that the front and side faces repeat themselves. the total surface area is:
[tex]A=2A_{tz}+A_{uf}+A_{lf}+2A_{sf}[/tex]
replacing the values:
[tex]A=2(28ft^2)+(90ft^2)+(40ft^2)+2(50ft^2)[/tex]
Solving the operations:
[tex]A=286ft^2[/tex]
Therefore, the surface area is 286 square feet.
