Question

Mark is roofing an old gymnasium that measures 270’x390’, and needs to calculate how many “squares “ he will need.(1 “square=100 ft square). The gym’s roof is a standard gable roof with 3’ of overhang on all sides. The roof angle measures 22.55 degrees from horizontal. How many squares of roofing does mark need ?

Answer 1

First, because of the roof having an inclination, we need to calculate the lenght of the surface we want to roof. The width will be the same.

Let's take a look at the situation:

Since we're on a right triangle, we can say that:

`\cos (22.25)=(G)/(R)`

Solving for R,

`\begin{gathered} \cos (22.25)=(G)/(R)\rightarrow R\cos (22.25)=G \\ \\ \Rightarrow R=(G)/(\cos (22.25)) \end{gathered}`

Since we already know that the lenght of the gym's floor is 390',

`\begin{gathered} R=(390^(\prime))/(\cos (22.25)) \\ \\ \Rightarrow R=421.38^(\prime) \end{gathered}`

We get that the lenght of the surface we want to roof is 421.38'

Now, let's take a look at the surface we want to roof:

Since the roof is a standard gable roof with 3’ of overhang on all sides, we add 6' to each dimension:427

Our total roofing area would be:

`427.38^(\prime)\cdot276^(\prime)=117956.88ft^2`

We then divide this total area by the area of one of our "squares":

`(117956.88)/(100)=1179.56`

We round to the nearest integer from above, since we can't buy a fraction of a square.

(this is called ceiling a number)

`1179.56\rightarrow1180`

Therefore, we can conclude that Mark needs 1180 squares of roofing.