Ars Mathematica: Solución del problema 42

O S = 0.25, d = A B = \sqrt{2^{2} - 0.2 5^{2}} = 1.984 \Rightarrow c o s α = \frac{0.25}{2} = \frac{1}{8} \Rightarrow α = 1.445468

C_{1} = \frac{2 π 1}{2 π} (2 π - 2 α) = 2 (π - α) = 3.3922

C_{2} = \frac{2 π 0.75}{2 π} 2 α = 1.5 α = 2.1682

2 (π - α) + 1.5 α + 2 \sqrt{2^{2} - 0.2 5^{2}} = 9.5284

([A S T B] + [S O T]) 2 + [A r e a] + [A r e a] =

[1.984 \cdot 0.75 + \frac{1.984 \cdot 0.25}{2}] 2 + \frac{π \cdot 1^{2}}{2 π} (2 π - 2 α) + \frac{π \cdot 0.7 5^{2}}{2 π} 2 α =

= 0.472 + 1.6961 + 0.8131 = 5.981 m^{2}

Ars Mathematica