Answer:
#1Without the roof panels, the surface area (except for the open panel) is 176.25 sq. ft.
With the roof panels, the surface area (except for the open panel) is 196.67 sq. ft.
The area of the rectangular sections (the sides without gables) is given by 10*6 = 60 sq. ft. There are two of these sides, for a total of 2*60 = 120 sq. ft.
The gables are triangles, which have an area formula of
A = 1/2bh
For the gables, this is 1/2(1.5)(7.5) = 5.625 sq. ft. Since there are two of them, this makes 2*5.625 = 11.25 sq. ft.
The closed side under a gable has an area of 6*7.5 = 45 sq. ft.
The two roof panels have an area of (4 1/12)(2 1/2) each:
49/12(5/2) = 245/24
There are two of them, which makes 490/24 = 20.42 sq. ft.
Without the roof panels, we have 45+11.25+120 = 176.25 sq. ft.
With the roof panels, we have 45+11.25+120+20.42 = 196.67 sq. ft.
#2 Solar cells can transform solar energy into electric energy. In a sunny day, the average power the sun incides on earth is approximately 1,000 watts (heat). if we had a 100% efficient solar cell, it would mean that the total amount of sunlight energy would be transformed into electrical energy, i.e. 1,000 watts of power. Its efficiency could be 1000 watts(solar cells)/1000(sunlight)x100(to express it in percentage).
Since the solar cells that will be mounted in the roof will produce 41 watts per square meter, its efficiency is calculated by dividing 41 /1,000x100. This gives us an efficiency of 4.1%. In order to generate 1,000 watts of power, we will need to use a simple rule-of-three, described like the following:
if 41 watts are produced by the solar cells in 1 square meter, how many square meters will be needed to produce 1,000 watts?
i.e. 41 watts ----------- 1 sq meter
1,000 watts ------------ x
Finally, we can assume that the solar cell system will produce this amount of energy constantly during a full day cycle (using solar cells at day and batteries at night).
5.8