Plot - wire mesh

In your yard, you want to build a garden that you want to fence. On the boundary of the plot, a fence 16 meters long is built. We have no more wire mesh for the fence. What area in square meters will the fenced garden have if it has the shape of a rectangle with a side of 5 m, if it has the shape of a square, if it has the shape of a circle?

Final Answer:

S₁ =  15 m²
S₂ =  16 m²
S₃ =  20.3718 m²

Step-by-step explanation:

$$\begin{gathered} o=16\text{m} \\ a=5\text{m} \\ o=2(a+b) \\ b=o/2-a=16/2-5=3\text{m} \\ {S}_1=a\cdot b=5\cdot 3=15{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} o=4c \\ c=o/4=16/4=4\text{m} \\ {S}_2=c^2=4^2=16{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} o=2\pi \cdot r \\ r=o/(2\pi )=16/(2\cdot 3.1416)\doteq 2.5465\text{m} \\ {S}_3=\pi \cdot r^2=3.1416\cdot 2.5465^2=20.3718{\text{m}}^2 \end{gathered}$$

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