Field with vegetables

The field planted with vegetables has a rectangular isosceles triangle with a leg length of 24 m. At the triangle's vertices are rotating sprinklers with a range of 12 m. How much of the field sprinkler isn't irrigated?

Final Answer:

S =  61.81 m²

Step-by-step explanation:

$$\begin{gathered} a=24\text{m} \\ r=12\text{m} \\ {S}_1=\frac{a^2}{2}=\frac{24^2}{2}=288{\text{m}}^2 \\ {S}_2=\pi \cdot \frac{\alpha }{360°}{r}^2 \\ {S}_2=\pi \cdot \frac{90+45+45}{360}\cdot r^2=3.1416\cdot \frac{90+45+45}{360}\cdot 12^2\doteq 226.1947{\text{m}}^2 \\ S=S_1-S_2=288-226.1947=61.81{\text{m}}^2 \end{gathered}$$

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