A scale drawing of an American flag is 14 inches long and 6 inches tall.
The actual flag is 3 feet tall.
a. True or False, the scale of the drawing is 2 in. : 1 ft.
is it false?
b. What is the perimeter of the american flag in the scale drawing?
c. What is the area of the american flag in the scale drawing?
d. What is the perimeter of the actual American flag?
e. What is the area of the actual American flag?
well, the scale is clearly
6in : 3 ft = 2in:1ft
surely you know how to figure perimeter and area
a. False, the scale of the drawing is 2 in. : 1 ft. is incorrect.
To find the correct scale:
1 foot = 12 inches
So, the correct scale of the drawing would be 14 inches / (3 feet x 12 inches/foot) = 14/36 = 7/18 inches per foot.
b. To find the perimeter of the American flag in the scale drawing, we need to double the length and width of the drawing and then add them together.
Length in the scale drawing: 14 inches
Width in the scale drawing: 6 inches
Perimeter in scale drawing = 2(14 inches) + 2(6 inches) = 28 inches + 12 inches = 40 inches.
c. To find the area of the American flag in the scale drawing, we simply multiply the length and width.
Area in the scale drawing = 14 inches x 6 inches = 84 square inches.
d. The perimeter of the actual American flag can be found by using the scale. The scale is 2 in. : 1 ft., which means that every 2 inches in the drawing represents 1 foot in reality.
Perimeter in actual flag = (2 inches / 1 ft.) x (3 feet) x 2 = 6 feet x 2 = 12 feet.
e. The area of the actual American flag can be found by using the same scale. Again, every 2 inches in the drawing represents 1 foot in reality.
Area in actual flag = (2 inches / 1 ft.) x (3 feet) x (12 inches/foot) = 2 inches x 3 feet x 12 inches = 72 square feet.
a. To find out if the statement is true or false, we need to compare the dimensions of the scale drawing to the actual flag. First, let's convert the 6 inches tall scale drawing to feet since we need to compare it to the actual flag's height in feet.
6 inches = 6/12 = 0.5 ft
Now, let's compare the dimensions to see if the scale is accurate:
Scale drawing: Length = 14 inches, Height = 0.5 feet
Actual flag: Height = 3 feet
The statement "the scale of the drawing is 2 in. : 1 ft" means that for every 2 inches on the scale drawing, it represents 1 foot in real life. Is this true?
Comparing the height dimension:
In the scale drawing, the height of 0.5 ft is represented by 6 inches. According to the scale, 2 inches should represent 1 foot. However, in this case, we have 6 inches representing 0.5 feet, which is not proportional. So, the statement is false.
b. To find the perimeter of the American flag in the scale drawing, we need to add up the lengths of all the sides of the flag. Since we only have the dimensions of the scale drawing, we will calculate the perimeter based on those measurements.
Perimeter of the scale drawing = 2 * (length + height)
= 2 * (14 inches + 6 inches)
= 2 * 20 inches
= 40 inches
c. To find the area of the American flag in the scale drawing, we multiply the length by the height:
Area of the scale drawing = length * height
= 14 inches * 6 inches
= 84 square inches
d. To find the perimeter of the actual American flag, we need to scale up the lengths based on the scale given. The scale is 2 in. : 1 ft.
The scale drawing's length is 14 inches, which represents a certain length of the actual flag. We can calculate it as follows:
Length in feet = 14 inches / 2 (scale factor)
= 7 feet
Since the flag has 4 sides of equal length, the perimeter would be 4 times this length:
Perimeter of the actual flag = 4 * 7 feet
= 28 feet
e. Similarly, to find the area of the actual American flag, we need to scale up the dimensions based on the scale given.
The scale drawing's height is 0.5 ft, which represents a certain height of the actual flag. We can calculate it as follows:
Height in feet = 0.5 ft / 2 (scale factor)
= 0.25 ft
Area of the actual flag = length * height
= 7 feet * 0.25 feet
= 1.75 square feet