Annulus from triangle

Calculate the content of the area bounded by a circle circumscribed and a circle inscribed by a triangle with sides a = 25mm, b = 29mm, c = 36mm

Correct result:

S = 831.0003 mm²

Solution:

a = 25 mm b = 29 mm c = 36 mm c_{1} = \sqrt{a^{2} + b^{2}} = \sqrt{2 5^{2} + 2 9^{2}} = \sqrt{1466} mm ≐ 38.2884 mm c_{1} \neq c s = \frac{a + b + c}{2} = \frac{25 + 29 + 36}{2} = 45 mm A = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} = \sqrt{45 \cdot (45 - 25) \cdot (45 - 29) \cdot (45 - 36)} = 360 {mm}^{2} R = \frac{a \cdot b \cdot c}{4 \cdot A} = \frac{25 \cdot 29 \cdot 36}{4 \cdot 360} = \frac{145}{8} = 18.125 mm r = \frac{A}{s} = \frac{360}{45} = 8 mm S_{1} = π \cdot R^{2} = 3.1416 \cdot 18.12 5^{2} ≐ 1032.0623 {mm}^{2} S_{2} = π \cdot r^{2} = 3.1416 \cdot 8^{2} ≐ 201.0619 {mm}^{2} S = S_{1} - S_{2} = 1032.0623 - 201.0619 = 831.0003 {mm}^{2}

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