# 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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## Question:

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?

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

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