Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42 cm.
Let the third side of the triangle be x.
Perimeter of the given triangle = 42 cm
18cm+10cm+x=42
∴x=14cm
s=Perimeter2=42cm2=21cm
By Heron’s formula,
Area of a triangle = √s(s−a)(s−b)(s−c)
Area of the given triangle = √s(s−a)(s−b)(s−c)=(√21(21−18)(21−10)(21−14))cm2=(√21(3)(11)(7))cm2=21√11cm2