Question

On a U.S. flag that is 19 feet by 10 feet, theunion is 7 5/8 feet by 5 3/8 feet. For each question, firstestimate the answer and then compute the actualpercentage.What percentage of the flag is red? For the actualpercentage round to the nearest tenth of a percent.

Answer 1

We find the total area of the flag

$A=\text{length}\cdot width=19\cdot10=190$

Total area 190 ft^2

Next, we have 13 red and white stripes that have a height of 10/13 ft.

And 3 red stripes are 19 ft by 10/13 ft. So the area for a red stripe is:

$\begin{gathered} A=19\cdot\frac{10}{13}=\frac{190}{13}=14.61 \\ \end{gathered}$

Area a red stripe 14.61 ft^2

Also, we have 4 stripes that is (19 - 7 5/8)ft by 10/13 ft. Then, the area for a stripe is:

$A=(19-7\frac{5}{8})\cdot\frac{10}{13}=(19-\frac{61}{8})\cdot\frac{10}{13}=\frac{91}{8}\cdot\frac{10}{13}=\frac{910}{104}=8.75$

Area red stripe 8.75 ft^2

Therefore, the total area of red color of the flag is

$A=3\cdot14.61+4\cdot8.75=43.83+35=78.83$

Area of the flag is red 78.83 ft^2

Finally, we find the percentage,

190 ---> 100%

78.83 --> x %

$\begin{gathered} x\cdot190=100\cdot78.83 \\ x\cdot\frac{190}{190}=\frac{100\cdot78.83}{190} \\ x=\frac{7883}{190}=41.5 \end{gathered}$

Answer: percentage of the flag is red 41.5%