An artist makes a painting that is 12 feet by 9 feet. He paints a frame around the painting. The frame is 3 inches wide. What is the area of the frame?
Please provide formula for figuring out.
Answers (a)10.75ftsq(b)10.5ftsq
(c)12.96ftsq(d)5.3125ftsq
Thanks.
3 in = 1/4 ft
(12 + 1/4)(9 + 1/4) - (12*9) = ?
-93.75
To find the area of the frame, we need to subtract the area of the painting from the area of the entire frame including the painting.
First, let's convert the dimensions of the painting from feet to inches:
Length of the painting = 12 feet * 12 inches/foot = 144 inches
Width of the painting = 9 feet * 12 inches/foot = 108 inches
Next, we need to calculate the dimensions of the entire frame including the painting:
Length of the frame = Length of the painting + 2 * Width of the frame
Width of the frame = Width of the painting + 2 * Width of the frame
Substituting the given values:
Length of the frame = 144 inches + 2 * 3 inches = 144 inches + 6 inches = 150 inches
Width of the frame = 108 inches + 2 * 3 inches = 108 inches + 6 inches = 114 inches
Now, let's calculate the area of the frame including the painting:
Area of the frame = Length of the frame * Width of the frame
Area of the frame = 150 inches * 114 inches
Since the question asks for the area in square feet, we need to convert the area from square inches to square feet:
Area of the frame = (150 inches * 114 inches) / (12 inches/foot * 12 inches/foot)
Area of the frame = (150 inches * 114 inches) / 144 square inches/square foot
Finally, to find the area of the frame alone, we need to subtract the area of the painting from the calculated area of the frame:
Area of the frame alone = Area of the frame - Area of the painting
Comparing the calculated area with the given answer choices, it appears that option (c) 12.96ftsq is the closest match.