1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
RideAnS [48]
3 years ago
6

1. The prism-shaped roof has equilateral triangular bases. Create an equation that models the height of one of the roof's triang

ular 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 amount 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.

Mathematics
2 answers:
Nat2105 [25]3 years ago
8 0

2. if a a=25 ft, then the height is  (ft)

3. one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l the lateral Area of the roof is 3a*l

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.

So the total area found previously will be decreased by al

5. so the area now is

6. now a=25 and l=2a=50

Area=

=3041.3 (ft squared)

Mandarinka [93]3 years ago
7 0
1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is \frac{ \sqrt{3} }{2} a

2. if a a=25 ft, then the height is \frac{ \sqrt{3} }{2} a=\frac{ \sqrt{3} }{2} *25= \frac{1.732}{2}*25= 21. 7 (ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*( \frac{1}{2} *a* \frac{ \sqrt{3} }{2}a )=\frac{ \sqrt{3} }{2} a^{2}

so the total area of the roof is \frac{ \sqrt{3} }{2} a^{2} +3al

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al


5. so the area now is \frac{ \sqrt{3} }{2} a^{2} +2al

6. now a=25 and l=2a=50

Area=\frac{ \sqrt{3} }{2} a^{2} +2al=\frac{ \sqrt{3} }{2} * 25^{2}+2*25*50=25 ^{2}  (\frac{ \sqrt{3} }{2} +4)=625*4.866

=3041.3 (ft squared)

You might be interested in
A printing press can print 224 newspapers in 8 minutes. What is the unit rate
expeople1 [14]

Divide  224 by 8 and you will get 28.

6 0
3 years ago
A square pyramid has side lengths each measuring 8 centimeters. The height of the pyramid is 3 centimeters. What is the lateral
maks197457 [2]

Answer:

80

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the equation of the line that passes through the point (6,14) and is parallel to the line with the following equation? y
Gekata [30.6K]

Answer:

y=\displaystyle-\frac{4}{3}x+22

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept
  • Parallel lines always have the same slope (<em>m</em>)

<u>Determine the slope (</u><em><u>m</u></em><u>):</u>

<u />y=\displaystyle-\frac{4}{3}x -1<u />

The slope of the given line is \displaystyle-\frac{4}{3}, since it is in the place of <em>m</em> in y=mx+b. Because parallel lines always have the same slope, the slope of a parallel line would also be \displaystyle-\frac{4}{3}. Plug this into y=mx+b:

y=\displaystyle-\frac{4}{3}x+b

<u>Determine the y-intercept (</u><em><u>b</u></em><u>):</u>

y=\displaystyle-\frac{4}{3}x+b

To find the y-intercept, plug in the given point (6,14) and solve for <em>b</em>:

14=\displaystyle-\frac{4}{3}(6)+b\\\\14=-8+b\\b=22

Therefore, the y-intercept of the line is 22. Plug this back into y=\displaystyle-\frac{4}{3}x+b:

y=\displaystyle-\frac{4}{3}x+22

I hope this helps!

5 0
2 years ago
Which kind if triangle is shown? (1point)
Salsk061 [2.6K]
Hey there! :D

None of the sides are equal. We can tell this by just looking at it. If the side BC was a straight side, it would be a right triangle, but it is not. It doesn't have any right angles. 

It is a scalene triangle. It has no equal sides and no equal angles.

I hope this helps!
~kaikers
6 0
3 years ago
7) What is the area of the parallelogram.
monitta

Answer:

78

Step-by-step explanation:

A=base*height

10*7.8

8 0
2 years ago
Other questions:
  • The house sparrows population has decreased by 41% since 1977. The population is now approximately 6.5 million pairs of birds. W
    6·1 answer
  • What is 1.8333 written as a simplified fraction
    11·1 answer
  • 4x - 4 - 2x + 3 solve this problem
    11·1 answer
  • Sabe-se que no inventário periódico, o registro contábil do estoque de mercadorias ocorrerá apenas no final de um determinado pe
    13·1 answer
  • Three fourths of a page are read in 2 minutes how many are read in one minute?
    12·1 answer
  • Which is the graph of g(x)?
    14·1 answer
  • Find the difference between8÷15 and -−2÷3. Show all calculations in your final answer.
    10·1 answer
  • Jesus loves you all have a blessed morning
    7·1 answer
  • Lucy purchased a prepaid phone card for $30. Long distance calls cost 21 cents a minute using this card. Lucy used her card only
    12·1 answer
  • Use the coordinates of the labeled point to find the point-slope equation of the line
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!