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Find the area of a triangle whose sides are respectively 9 cm, 12 cm and 15 cm.

Question:

Find the area of a triangle whose sides are respectively 9 cm, 12 cm and 15 cm.

 

Solution:

Let the sides of the given triangle be a, b, c respectively.

So given,

a = 9 cm

b = 12 cm

c = 15 cm

By using Heron's Formula

The Area of the triangle $=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$

Semi perimeter of a triangle = s

2s = a + b + c

s = (a + b + c)/2

s = (9 + 12 + 15)/2

s = 18 cm

Therefore,

Area of the triangle $=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$

$=\sqrt{18 \times(18-9) \times(18-12) \times(18-15)}$

$=54 \mathrm{~cm}^{2}$

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