Sss triangle

Calculate the area and heights in the triangle ABC by sides a = 8cm, b = 11cm, c = 12cm

Correct result:

S =  42.7895 cm2
h1 =  10.6974 cm
h2 =  7.7799 cm
h3 =  7.1316 cm

Solution:

a=8 cm b=11 cm c=12 cm  s=(a+b+c)/2=(8+11+12)/2=312=15.5 cm S=s⋅ (s−a)⋅ (s−b)⋅ (s−c)=15.5⋅ (15.5−8)⋅ (15.5−11)⋅ (15.5−12)=42.7895 cm2
S=a⋅ h12 h1=2⋅ S/a=2⋅ 42.7895/8=10.6974 cm
h2=2⋅ S/b=2⋅ 42.7895/11=7.7799 cm
h3=2⋅ S/c=2⋅ 42.7895/12=7.1316 cm

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