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Solution:

Let the given perimeter P = 30 cm and the two equal sides a = b = 12 cm.
Let the third side be denoted by c.
Now, we know that, perimeter of triangle = sum of all sides
So, P = a + b + c
30 = 12 + 12 + c

Hence, c = 6 cm.
30
Now, s = Perimeter of triangle = = 15 cm.
2 2
Now, using Heron‟s formula,
Area of triangle =

=

= 15 × 3 × 3 × 9

= 5 × 3 × 3 × 3 × 3 × 3

2
2
=9 15 = (9× 3.87) =34.83
2

Example-7

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

Solution:

Assume the third side of the triangle to be “x”.

Now, the three sides of the triangle are 18 cm, 10 cm, and “x” cm

It is given that the perimeter of the triangle = 42cm

So, x = 42 – (18 + 10) cm = 14 cm

42
∴ The semi perimeter of triangle = = 21 cm
2
Using Heron‟s formula,

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