A scale drawing of a living room is shown below. The scale is 1 : 40.
A rectangle is shown. The length of the rectangle is labeled 6 inches. The width of the rectangle is labeled 4 inches.
Show your work to determine the area of the room in square feet. (5 points)
actual length = 240 inches = 20 ft
actual width = 160 inches = 40/3 ft
actual area = 20(40/3) ft^2
= 800/3 ft^2
actual length = 240 inches = 20 ft
actual width = 160 inches = 40/3 ft
actual area = 20(40/30) ft^2
= 800/3 ft^2
To determine the area of the room in square feet, we first need to convert the measurements given in inches to feet, since the area should be in square feet.
Since the scale is 1:40, it means that each inch on the drawing represents 40 inches in real life. To convert inches to feet, we need to divide by 12, since there are 12 inches in 1 foot.
So, for the length of the room:
6 inches ÷ 12 inches/foot = 0.5 feet
And for the width of the room:
4 inches ÷ 12 inches/foot = 0.33 feet (rounded to two decimal places)
Now that we have the length and width of the room in feet, we can calculate the area of the room by multiplying the length by the width:
Area = Length × Width
Area = 0.5 feet × 0.33 feet
Area = 0.165 square feet (rounded to three decimal places)
Therefore, the area of the room is approximately 0.165 square feet.