The A& N painting Co. was hired to paint the inside of a community center building that has 4 units. each unit is an activity room in the shape of a rectangular solid with a length of 30 feet and a width of 20 feet. the ceilings are 9 feet tall. assuming that they do not have to paint the floor or ceiling, how many square feet of wall space is there that needs to be painted?

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Mathematics

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24 August, 07:20

The A& N painting Co. was hired to paint the inside of a community center building that has 4 units. each unit is an activity room in the shape of a rectangular solid with a length of 30 feet and a width of 20 feet. the ceilings are 9 feet tall. assuming that they do not have to paint the floor or ceiling, how many square feet of wall space is there that needs to be painted?

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Luna Maynard · Answer 1

Each room has width a, length b and heigth c. Let's use following formulas for area:

Floor and ceiling:

A1=a*b

Left and right wall:

A2=b*c

Front and back wall:

A3=a*c

a=30ft

b=20ft

c=9ft

We do not need to paint floor and ceiling, so total area that needs to be painted is:

A (unit) = 2*A2+2*A3

A (unit) = 2*b*c+2*a*c

A (unit) = 2*20*9+2*30*9

A (unit) = 360+540

A (unit) = 900ft^2

We have 4 units so total area that needs to be painted is:

A (total) = 4*A (unit)

A (total) = 4*900

A (total) = 3600ft^2