1. the prism-shaped roof has equilateral triangular bases. create an equation that models the height of one of the roof's triangular bases in terms of its sides. in your final answer, include all necessary calculations.

2. the prism-shaped roof has equilateral triangular bases. use the model you created in question #1 to calculate the height of the roof, to the nearest tenth of a foot, if the side lengths each measure 25 feet. in your final answer, include all necessary calculations.

3. to determine the number of roofing materials needed, the area of the roof's entire surface is calculated, including the ceiling of the garage. considering the sketch of the roofing design, create a formula to model the area of the roof's entire surface. in your final answer, include all of your calculations.

4. the contractor in charge of the roofing project is trying to make the job the most cost-effective for the homeowners. in order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. in other words, there will not be a barrier built between the garage and the roof. in two or more complete sentences, explain how these changes affect the model for the area of the roof's entire surface.

5. the contractor in charge of the roofing project is trying to make the job the most cost effective for the homeowners. in order to cut back on the cost of supplies, he decides that a ceiling in the garage is not necessary. in other words, there will not be a barrier built between the garage and the roof. create a formula modeling the area of the roof’s surfaces that the contractor will be purchasing supplies for.

6. use the formula you created in the previous question to calculate the area of the roof that the contractor will be purchasing supplies for, assuming that the side length of the triangular bases is 25 feet and the length of each rectangular face is twice its width.

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