Question

I need help on how to find a surface area! I will send the full photo!

Answer 1

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:

`A_(tz)=(b+B)/(2)h`

Where "b" is the upper base, "B" is the lower base and "h" is the height. Replacing the values:

`A_(tz)=(9ft+4ft)/(2)*4.3ft`

Solving the operations:

`A_(tz)=28ft^2`

the upper face is a rectangle, its area is the product of its side:

`A_(uf)=(10ft)(9ft)=90ft^2`

The area of the lower face is also a rectangle, therefore its area is:

`A_(lf)=(4ft)(10ft)=40ft^2`

The side face is also a rectangle, and its area is:

`A_(sf)=(5ft)(10ft)=50ft^2`

Now we add the areas having into account that the front and side faces repeat themselves. the total surface area is:

`A=2A_(tz)+A_(uf)+A_(lf)+2A_(sf)`

replacing the values:

`A=2(28ft^2)+(90ft^2)+(40ft^2)+2(50ft^2)`

Solving the operations:

`A=286ft^2`

Therefore, the surface area is 286 square feet.