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:
[tex]\begin{gathered} A_u=(7+\frac{5}{8})\cdot(5+\frac{3}{8}) \\ A_u=(\frac{7\cdot8+5}{8})\cdot(\frac{5\cdot8+3}{8}) \\ A_u=(\frac{56+5}{8})\cdot(\frac{40+3}{8}) \\ A_u=\frac{61}{8}\cdot\frac{43}{8} \\ A_u=\frac{61\cdot43}{64} \\ A_u\approx43 \end{gathered}[/tex]
Then, we can now calculate the area of the flag as:
[tex]A_f=19\cdot10=190[/tex]
We can now estimate the percentage as:
[tex]p=\frac{A_u}{A_f}\approx\frac{43}{190}\approx\frac{45}{200}\approx0.225=22.5\%[/tex]
We can now calculate the values with a calculator as:
[tex]A_u=\frac{61\cdot43}{64}\approx40.98[/tex]
Then, the percentage is:
[tex]p=\frac{A_u}{A_f}\approx\frac{40.98}{190}\approx0.2157\approx21.6\%[/tex]
Answer:
The estimated percentage was 22.5%.
The actual percentage is 21.6%.
