# Find the area of a triangle with sides 4, 5 and 6

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Let abc be a triangle such that:

a= 4

b= 5

c= 6

Then the perimeter is:

P = a + b + c = 4 + 5 + 6 = 15

==> P = 15

But we know that the area :

A = sqrt[P/2 (p/2 - a)(p/2 - b) (p/2 - c)]

= sqrt[(7.5)*(3.5)*(2.5)*(1.5) ]

= sqrt(98.4375)

** = 9.92 square units (approx.)**

The sides of the triangle are a =4, b= 5 and c = 6.

We use the Heron's formula , Area A = sqrt{s(s-a)(s-b)(s-c)} ,as 3 sides of the triangle are given.

s = (a+b+c)/2 = (4+5+6)/2 = 7*5

Therefore A = sqrt{7.5(7.5-4)(7.5-5)(7.5-6)}

A= sqrt{7.5*3.5*2.5*1.5}

A= 9.9216 sq units approximately.

We can find the area of a triangle in terms of its semi perimeter and the sides.

If the semi perimeter, s = (a + b + c)/2 = (4+5+6)/2 = 15/2

The area of the triangle can be found using the relation Area = sqrt [ s*(s-a)*(s-b)*(s-c)]

sqrt [ s*(s-a)*(s-b)*(s-c)]

=> sqrt [(15/2)*((15/2) – 4)*((15/2)-5)*((15/2)-6)]

=> sqrt [(15/2)*(7/2)*(5/2)*(3/2)]

=> sqrt [98.4375]

=> 9.92 (approximately)

**The area of the triangle is approximately 9.92.**