**Class 9 Exercise 12.1 Question 4**

**find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is ****42cm . **

**Solution: **Let and be the sides of the triangle ABC.

Here we have perimeter of the triangle , and .

First we will find the 3rd side of the triangle by using perimeter, then we will use ** Heron’s formula** to find the area of the given triangle.

The ** Heron’s formula ** for finding the area of a triangle given by

Area of a triangle = |

where , and are the sides of the triangle and s= semi-perimeter i.e. half of the perimeter of the triangle= .

It is given that . Putting the value of and , we get

18+10+=42

Now semi-perimeter

So

Therefore , area of the triangle =

=

=

**Area of triangle =** .

Conclusion: The area of the triangle two sides of which are 18 cm and 10 cm and the perimeter is

42 cm is .