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.1. What percentage of the flag is taken up by theunion? For the actual percentage round to the nearesttenth of a percent. Show work on the sketch.

Answer 1

We have to estimate and then calculate the proportion, in percentage, of the flag is the union area.

We can estimate the area of the union as:

`\begin{gathered} A_u=(7+(5)/(8))\cdot(5+(3)/(8)) \\ A_u=((7\cdot8+5)/(8))\cdot((5\cdot8+3)/(8)) \\ A_u=((56+5)/(8))\cdot((40+3)/(8)) \\ A_u=(61)/(8)\cdot(43)/(8) \\ A_u=(61\cdot43)/(64) \\ A_u\approx43 \end{gathered}`

Then, we can now calculate the area of the flag as:

`A_f=19\cdot10=190`

We can now estimate the percentage as:

`p=(A_u)/(A_f)\approx(43)/(190)\approx(45)/(200)\approx0.225=22.5\%`

We can now calculate the values with a calculator as:

`A_u=(61\cdot43)/(64)\approx40.98`

Then, the percentage is:

`p=(A_u)/(A_f)\approx(40.98)/(190)\approx0.2157\approx21.6\%`

Answer:

The estimated percentage was 22.5%.

The actual percentage is 21.6%.