A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also, find the smallest of its altitudes.
Let a, b and c are the sides of triangle and s is the semi-perimeter, then its area is given by:
A = 
where 
[Heron’s Formula]
= 
= 75
A = 
A = 
= 
cm2
Altitude on side 35 cm:
Area of triangle = 
939.15 = 
Altitude = 53.66 cm
Altitude on side 54 cm:
Area of triangle = 
939.15 = 
Altitude = 34.78 cm
Altitude on side 61 cm:
Area of triangle = 
939.15 = 
Altitude = 30.79 cm
Therefore smallest Altitude is: 30.79 cm
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