A scale drawing of an American flag is 10 inches long and 6 inches tall. The actual flag is 3 ft tall.
Find the actual perimeter and area of the American flag. Show your work.
To find the actual perimeter and area of the American flag, we need to use the given scale drawing and the ratio between the dimensions of the scale drawing and the actual flag.
First, let's calculate the ratio between the height of the scale drawing and the actual height of the flag:
Ratio = Actual Height / Scale Height
Ratio = (3 ft) / (6 inches) [1 ft = 12 inches]
Ratio = (3 ft) / (0.5 ft) [since 0.5 ft = 6 inches]
Ratio = 6
So, the actual height of the flag is 6 times the height of the scale drawing.
Next, let's calculate the ratio between the width of the scale drawing and the actual width of the flag. Since the width is not given for the scale drawing or the actual flag, we can assume that the flag's proportions match those specified in the flag code. The ratio of the width to the height of the American flag is approximately 1:1.9.
Therefore, the ratio between the width of the scale drawing and the actual width of the flag can be estimated as 1:1.9 as well.
Now, let's calculate the actual width of the flag using the ratio we assumed:
Actual Width = Ratio * Scale Width
Actual Width = 1.9 * 10 inches [since the scale width is given as 10 inches]
Actual Width = 19 inches
Thus, we have determined that the actual dimensions of the flag are 19 inches wide and 3 feet tall.
Now, let's calculate the actual perimeter of the flag.
Perimeter = 2*(Actual Width + Actual Height)
Perimeter = 2*(19 inches + 3 ft) [converting 3 ft to inches: 1 ft = 12 inches]
Perimeter = 2*(19 inches + 36 inches)
Perimeter = 2*(55 inches)
Perimeter = 110 inches
Therefore, the actual perimeter of the American flag is 110 inches.
Finally, let's calculate the actual area of the flag.
Area = Actual Width * Actual Height
Area = 19 inches * 36 inches [since 3 feet = 36 inches]
Area = 684 square inches
Hence, the actual area of the American flag is 684 square inches.
3ft : 6in is a scale of 6:1
So, the flag's perimeter is 6 times as big as the drawing's.
The drawing's perimeter is 2*(10+6) inches, so ...