SOLUTION: Hello! I am currently doing a project for an Environmental Science class. We are studying ways to save energy. I have been asked to give the measurements of my home. I am runni

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Question 65021: Hello! I am currently doing a project for an Environmental Science class. We are studying ways to save energy. I have been asked to give the measurements of my home.
I am running into a problem when I try to give the area of the walls and also the area of the ceilings (total). I have 1,100 square feet in my home. It would not be so bad if I had just all 8 ft. ceilings. However, in the 18x13 living room I have a vaulted ceiling reaching 13 feet. (All of the other rooms have 8ft.) I am sure I am just making this difficult. I need to use the Pythagorean Theorem to figure this out, but seem to come up with answers that do not make sense.
Can you help?
Answer by 303795(602) (Show Source):
You can put this solution on YOUR website!
Using the data given I have made the following assumptions.
1. The sides of this room are 8ft high.
2. The 13 ft side is the one reaching to 13 ft.
3. The extra surface on the 13 ft side is triangle shaped.
4. The 13 ft height is in the middle of the 13 ft end.
The extra surface area at one end of the room is in the shape of a triangle
=1/2 base * height
=1/2 * 13 * 5
=32.5 square feet
Same at the other end gives 65 square feet in the ends.

The hypotenuse at the end will be the length of the roof section on each side of the room.
Hyp = sqrt(6.5^2 + 5^2)
=8.2 feet.
The area of a single side of the roof will be 18 * 8.2 = 148 square feet. Double this for the two sides of the roof = 296

The area of the plain roof at a height of 8 feet would be 18 x 13 = 234 square feet. The area of the ceiling and extra ends is 371 square feet. So you have an extra 137 square feet in the room because of the ceiling design.
If my assumptions of the room design are incorrect use the general idea to work out the area.