An equilateral

An equilateral triangle with a side of 10 m represents a wooden platform standing on a lawn. A goat is tied to a corner with a 15 m rope. What is the maximum amount of grazing area available to the goat?

Correct answer:

S =  663.5571 m²

Step-by-step explanation:

$$\begin{gathered} a=10\text{m} \\ r=15\text{m} \\ {S}_1=\sqrt{3}/4\cdot a^2=\sqrt{3}/4\cdot 10^2=25\sqrt{3}{\text{m}}^2\doteq 43.3013{\text{m}}^2 \\ {S}_2=\pi \cdot r^2=3.1416\cdot 15^2\doteq 706.8583{\text{m}}^2 \\ r>a \\ S=S_2-S_1=706.8583-43.3013=663.5571{\text{m}}^2 \end{gathered}$$

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