Percentage 80164

I was given a square ABCD 4.2 cm. Find the set of all points that have a distance less than or equal to 2 cm from one of its vertices and lie inside this square. Indicate how much of the square this area occupies as a percentage.

Correct answer:

p =  71.2379 %

Step-by-step explanation:

$$\begin{gathered} a=4.2\text{cm} \\ r=2\text{cm} \\ {S}_2=a^2=4.2^2=\frac{441}{25}=17.64{\text{cm}}^2 \\ {S}_1=\pi \cdot r^2=3.1416\cdot 2^2\doteq 12.5664{\text{cm}}^2 \\ p=100\cdot \frac{S_1}{S_2}=100\cdot \frac{12.5664}{17.64}=71.2379\% \end{gathered}$$

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