Answer:
Step-by-step explanation:
A barn is in form of rectangular prism
Given the dimension
Height H = 20 ft
Length L = 84 ft
Width W = 38 ft
Triangular prism dimensions
Height H = 12 ft
Length L = 84 ft
Width W = 19 ft
Given that,
1 gallon covers 232 Square feet
1 gallon = 232 ft²
So, we need to total surface area to be shaded
First for the rectangular prism, only the four exteriors wall that can be painted, the bottom and the top where the triangular rest on cannot be painted,
So, Area of rectangular prism
A = 2(LW + LH + WH)
But in this case, no length and width covers so, LW = 0
A = 2(LH + WH)
A1 = 2(84 × 20 + 38 × 20)
A1 = 2(1680 + 760)
A1 = 2 × 2440
A1 = 4880 ft²
Now, area to be covered in the triangular prism
Only two regular face is needed to be covered
Then,
Area of a triangle is ½b×h
Then, the two sides to be cover will have
A2 = 2 × (½ × 19 × 12)
A2 = 228ft²
So, total area to be painted is
A = A1 + A2.
A = 4880 + 228
A = 5108 ft²
So,
1 gallon = 232ft²
x gallon = 5108ft²
Cross multiply
x gallon = 5108ft² × 1gallon / 232ft²
x gallon = 22.017
So, approximate 22 gallon will be enough, but for design reason, it is advisable to get 23 gallons,
