Percentage 24151

In a square garden with a side length of 12 m, there are two circular flower beds with a diameter of 4 m, and the rest is grass. Determine the area that is overgrown with grass. What percentage of the garden is occupied by flower beds?

Correct answer:

t =  118.8673 m²
k =  17.4533 %

Step-by-step explanation:

$$\begin{gathered} a=12\text{m} \\ D=4\text{m} \\ r=D/2=4/2=2\text{m} \\ {S}_1=a^2=12^2=144{\text{m}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 2^2\doteq 12.5664{\text{m}}^2 \\ t=S_1-2\cdot S_2=144-2\cdot 12.5664=118.8673{\text{m}}^2 \end{gathered}$$

$k=100\cdot \frac{2\cdot S_2}{S_1}=100\cdot \frac{2\cdot 12.5664}{144}=17.4533\%$

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