Answer:
the total number of shingles is 3060
Step-by-step explanation:
Please have a look at the attached photo.
We need to find the total are of the roof.
The are of the trapezoid is:
- A = 1/2 (base 1 + base 2) height
= 1/2 (20+30)*15
= 375 [tex]ft^{2}[/tex]
The are of the triangle:
= 1/2(1.5*10)
= 7.5 [tex]ft^{2}[/tex]
=> We need to find the total are of the roof is:
The are of the 2 trapezoids + The are of the 2 triangles
= 375 [tex]ft^{2}[/tex]*2 + 7.5 [tex]ft^{2}[/tex] *2
= 765 [tex]ft^{2}[/tex]
Given in the question that, the shingles are 1 foot by 1 foot, but they overlap by 0.75 square foot so the usable area of the shingle is only 0.25 [tex]ft^{2}[/tex]
So the total number of shingles is:
765 [tex]ft^{2}[/tex] / 0.25 [tex]ft^{2}[/tex]
= 3060
