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18 September, 11:17

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.

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  1. 18 September, 13:43
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    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,
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