Field with vegetables

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

Result

S =  61.81 m2

Solution:

S1=a22=2422=288 m2 S2=πα360r2 S2=π90+45+45360122 S2=π/2122=226 m2  S=S1S2=61.81 m2S_1 = \dfrac{a^2}{2} = \dfrac{24^2}{2} = 288 \ m^2 \ \\ S_2 = \pi \dfrac{ \alpha }{ 360^\circ } r^2 \ \\ S_2 = \pi \dfrac{ 90+45+45 }{ 360^\circ } 12^2 \ \\ S_2 = \pi /2 \cdot 12^2 = 226 \ m^2 \ \\ \ \\ S = S_1 - S_2 = 61.81 \ m^2



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