Lunes of Hippocrates

Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the areas of the lunas with the area of the triangle ABC.

Correct answer:

S =  24 cm2

Step-by-step explanation:

a=6 cm b=8 cm  c=a2+b2=62+82=10 cm R=c/2=10/2=5 cm  S1=2a b=26 8=24 cm2  Sa=π (a/2)2/2=3.1416 (6/2)2/214.1372 cm2 Sb=π (b/2)2/2=3.1416 (8/2)2/225.1327 cm2 Sc=π R2/2=3.1416 52/239.2699 cm2  S2=ScS1=39.26992415.2699 cm2  S=Sa+SbS2=14.1372+25.132715.2699=24 cm2  S=S1 = 2a b=24 cm2

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