A barn is shaped like a rectangular prism with a triangular prism on top as shown. The exterior four walls and two triangular faces need to be repainted. If one gallon of paint covers 232 square feet, how many gallons will it take to repaint the barn? Enter your answer in the box.

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,