A scale drawing of an American flag is 10 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.
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?
This is a question about scaling. The scale drawing is 10 inches long and 6 inches tall. Draw a figure to help you visualize the problem.
The actual flag is 3 feet or 36 inches tall. The scaled drawing is 1/6 the size of the actual flag. The actual flag is 36 inches tall and 60 inches long.
a. False, the scale of the drawing 1/6 of the actual flag.
b. The perimeter is total length of all the sides combined. Therefore, the total side length, or perimeter, of the scaled drawing is 32 inches (10+10+6+6).
c. The area of the flag is the product of the lengths. The area of the scale drawing is 60 square inches (6x10).
d. The perimeter of the actual flag is 156 inches (36+36+60+60).
e. The area of the actual flag is 2160 square inches (36x60).
Note: Area doesn't scale by a factor of six, rather 6^2 because area is square inches.
a. Is TRUE. The test isnt asking for the scale factor, its just asking for the scale. So therefore 1:6 is incorrect. The real answer is 2in:1ft
e. Is actually 15ft squared.
I am a teacher and i have done this test and know the actual answers these are the corrections to the previous answers by anonymous.
a) True, 3 feet: 6 inches = 1 foot: 2 inches
b) 10+10+6+6 = 32 inches perimeter
c) 10 x 6 = 60 inches^2 area (^2 means squared)
d) Scale is 1ft:2inches so 'n' ft:32inches. 32/2= 16. Perimeter of actual flag is 16 inches.
e) 30
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To solve these problems, we need to understand the concept of scale and use some mathematical formulas. Let's go step by step:
a. To determine if the scale is 2 in. : 1 ft., we can compare the vertical dimensions of the drawing and the actual flag.
The height of the scale drawing is given as 6 inches.
The actual height of the flag is 3 feet, which is equal to 36 inches.
Therefore, we can calculate the scale ratio by dividing the actual height by the drawing height:
36 inches / 6 inches = 6
Since we got a ratio of 6, this means the scale is 6 in. : 1 ft.
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. Since the scale drawing is rectangular, we can find the perimeter by doubling the sum of its length and width.
Length of the drawing = 10 inches
Width of the drawing = 6 inches
Perimeter of the drawing = 2 * (Length + Width) = 2 * (10 inches + 6 inches) = 2 * 16 inches = 32 inches
c. To find the area of the American flag in the scale drawing, we need to multiply its length by its width.
Area of the drawing = Length * Width = 10 inches * 6 inches = 60 square inches
d. To find the perimeter of the actual American flag, we need to convert the scale drawing's measurements to the actual measurements. Since the scale is 6 in. : 1 ft., we can convert inches to feet by dividing them by 12.
Length of the drawing = 10 inches
Width of the drawing = 6 inches
Length of the flag = (10 inches / 12) feet = 0.8333 feet (rounded to four decimal places)
Width of the flag = (6 inches / 12) feet = 0.5 feet
Perimeter of the flag = 2 * (Length + Width) = 2 * (0.8333 feet + 0.5 feet) = 2 * 1.3333 feet = 2.6666 feet (rounded to four decimal places)
e. To find the area of the actual American flag, we need to multiply its length by its width.
Length of the actual flag = 3 feet
Width of the actual flag = (9/13) times the width of the actual flag
Area of the actual flag = Length * Width = 3 feet * [(9/13) * width of the actual flag feet]
Since we don't have the width of the actual flag, we cannot calculate its area.