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Question

A room needs to be painted. the four walls and ceiling need to be covered. There are 2 windows 2' x 3' and one door 6'-8" tall and 32" wide. Subtract the area for the windows and door. Front to back is 15'- 6", side to side is 13'-9 and the walls are 96" tall. How many square feet needs to be covered to the nearest foot?

Answer 1

2x2x3 = 12 ft^2 = window areas

6'8" x32" = 6 2/3 x 2 2/3 = 20/3)(8/3) = 160/9 ft^2 = 17 2/3 ft^2 = door areas

15'6" x 13'9" = 15 1/2 x 13 3/4 = 31/2 x 55/4 = 1705/8 = 213 1/3 ft^2 = ceiling area

2x 15'6" x 96" = 2(31/2)(8) =31(8) = 248 ft^2 = 2 side areas

2x13'9" x 96" = 2(55/4)(8)= 4(55) = 220 ft^2 = the other 2 side areas

total area = 220+248+213 1/3 - 17 2/3 -12 = 681 -29 2/3 = 651 1/3 ft^2

(no guarantees on error free calculations, but that's the basic method)

round to nearest square foot

= 651

Answer 2

Step 1) convert everything into feet:

Windows: (already in feet) 2 ft x 3 ft

Door: 6 ft 8 inches = 6 + 8/12 = 8.66667 ft and 32 inches = 32/12 = 3.66667 ft

Walls: Front-to-back = 15 ft 6 inches = 15 + 6/12 = 15.5 ft and side-to-side = 13 ft 9 inches = 13 + 9/12 = 13.75 ft, and height = 96 inches = 96/12 = 8 ft

Step 2) Calculate area of walls and ceiling:

Wall 1: width x height = (15.5)(8) = 124 sq ft

Wall 2: width x height = (13.75)(8) = 110 sq ft

Wall 3: width x height = (15.5)(8) = 124 sq ft

Wall 4: width x height = (13.75)(8) = 110 sq ft

Ceiling: width x length = (15.5)(13.75) = 213.125 sq ft

Add all walls and ceiling: 124 + 110 + 124 + 110 + 213.125 = 681.125 sq ft

Step 3) Calculate area of windows and door to subtract:

Window 1: width x height = (2)(3) = 6 sq ft

Window 2: width x height = (2)(3) = 6 sq ft

Door: width x height = (8.66667)(3.66667) = 17.77778 sq ft

Add all windows and door: 6 + 6 + 17.77778 = 29.77778 sq ft

Step 4) Calculate total area by subtracting door/windows from walls/ceiling: 681.125 - 29.77778 = 651.3472 sq ft

Step 5) Round to the nearest sq ft = 651 sq ft