The total surface area of doghouse with including the floor and door of the doghouse is 56 feet squared.
What is surface area?
Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.
It is given that the length of the triangular side of doghouse is 2.5 feet.
The length of the base is 4 feet and the side of the base is 3 feet.
Area of top side of dog house-
- The top triangular roof of the doghouse consist the four triangular faces.
- Two faces of front side and back side has the height 2 feet and base 3 feet long similar to floor width
- The left and right side has height 2.5 feet and base 4 feet long similar to floor length.
Thus, the total surface area of the top triangular roof of the doghouse is,
[tex]A_{top}=2\times\dfrac{1}{2}\times 2\times3+2\times\dfrac{1}{2}\times 2.5\times4\\A_{top}=16 \rm ft^2[/tex]
Area of bottom side of dog house-
- The bottom cuboid roof of the doghouse consist the four rectangular faces.
- Two faces of front side and back side has the height 2 feet and base 3 feet long.
- The left and right side has height 2 feet and base 3 feet long.
Thus, the total surface area of the bottom rectangular faces of the doghouse is,
[tex]A_{bottom}== 2\times2\times3+2\times2\times4\\A_{bottom}=28\rm ft^2[/tex]
The surface area of floor with dimensions 3 ft and 4 ft is,
[tex]A_f=4\times3\\A_f=12\rm ft^2[/tex]
The total surface area of the doghouse is,
[tex]A=\A_{top}+A_{bottom}+A_f\\A=16+28+12\\A=56\rm ft^2[/tex]
Thus, the total surface area of doghouse including floor and door is 56 feet squared.
Learn more about the surface area here:
https://brainly.com/question/20771646
