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
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
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 .