A triangle has sides 35 cm 54cm and 61 cm long. Find it's area also find the smallest altitude.

Let the sides be a, b and c

∴ sides of triangle area = 35cm, b = 54cm, c = 61cm.

∴ by Heron’s formula, we get the area of a triangle

=

(where s = s is called as the semi perimeter)…(1)

∴ we get

Substituting the value of s, a, b and c in equation 1 we get

⇒

=

=

∴ The area of a triangle is .

Find the smallest altitude,

The smallest altitude has the largest base.

∴ The side which is largest has the smallest altitude.

largest side = base = 61 cm

Now the area of a triangle having base and altitude is given by

=

=