Question

an architect creates a rough blue print for a new warehouse. how many square feet of carpet will you need? if you paint the interior walls how much are will you cover? how many square feet of shingles will you need to cover the roof? you decide to divide the warehouse into 2 rooms by building a vertical wall to the peak of the roof. what is the area of the larger room?

Answer 1

To solve this problem, we first have to find the dimensions of the front triangle, we are going to use the fact that it is a rectangle triangle, I am going to draw please wait a moment

Solving the rectangle triangle, using the trigonometric functions

`\begin{gathered} \sin \text{ (55)= }(b)/(150)\text{ }\Rightarrow\text{ b=}150\cdot\text{ sin(55) = 122.87 } \\ \cos (55)=\text{ }(a)/(150)\Rightarrow\text{ a= 150}\cdot\cos (55)\text{ = 86.08 } \end{gathered}`

Now with that information we can start answering all the questions.

1.- For this questions we have to calculate the area of the floor, in this case is a rectangle with dimensions 150ft and 75ft so we multiply and get that we need 11250 ft^2 of carpet.

2.- In this questions we have to calculate the total area of the walls, once again we have to deal with rectangles and now with the triangles of the ceiling. I am going to draw a picture to ilustrate please wait a moment

We have 4 rectangles, 2 of them have dimensions 75ft and 30ft, the other 2 have dimensions 150ft and 30ft, so we multiply as before we get a total area of 13500ft^2.

Now we calculate the area of the triangles and add them ( remember is 2 triangles the one in the front and the one in the back) , we do this with the usual formula for the area of a triangle and get 10574.19 ft^2.

Finally adding both areas we get, 24074.19ft^2.

3.- For this questions we need to calculate the area of the roof which is the remaining area of the ceiling that we didn't count as walls, for this you have to remember that in the begining we calculated a and b. Notice that these are rectangles, one of area 75*a and the other one is 75*b. Substituting the values of a and b we found earlier ( and adding the areas of both rectangles together) we get that the total area of the roof is 15671.25ft^2

4.- For this questions I am going to draw a picture to ilustrate

Notice that d1=cos(55)*a = 49.37ft then the dimensions of the bigger room are 150ft-49.37ft=100.63 ft and 75ft so the floor area is 100.63ft*75ft = 7547.25 ft^2