JonahnatoR0
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Bernie is designing his dream home. His design includes space for his painting studio in the attic. The attic of the house is shaped like a triangular prism, and the roof has two sloping rectangular sides. Bernie wants the attic to have at least 1,200 square feet of floor space and to be at least 10 feet tall in the middle to give him plenty of room to stand up while working. The width of the attic will be 24 feet.

If the shingles for the roof cost $4.25 per square foot to install, what is the minimum cost for installation in a design that meets Bernie's requirements?



Answer :

spook8

Answer:

To find the minimum cost for shingle installation, we need to calculate the total area of the roof.

The area of each sloping rectangular side of the roof can be calculated as follows:

Area = length * width

Since the width is given as 24 feet and the height in the middle is at least 10 feet, we can use the Pythagorean theorem to find the length of each side: in

Length = sqrt(10^2 + 24^2) = sqrt(100 + 576) = sqrt(676) = 26 feet

Now, we can find the area of each sloping side:

Area_sloping_side = 26 feet * 24 feet = 624 square feet

Since there are two sloping sides, the total area of the sloping roof is:

Total_area_sloping_roof = 2 * Area_sloping_side = 2 * 624 square feet = 1248 square feet

The total area of the roof is the sum of the area of the two sloping sides and the floor area of the attic:

Total_area_roof = Total_area_sloping_roof + 1200 square feet = 1248 square feet + 1200 square feet = 2448 square feet

Now, we can find the cost for installation:

Cost = Total_area_roof * $4.25/square foot

Cost = 2448 square feet * $4.25/square foot = $10,420

So, the minimum cost for shingle installation in Bernie's design is $10,420.

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