What is the area of the triangle if the sides are 3,5, and 6.

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We have the sides of the triangle given as 3, 5 and 6.

We find the area using Heron's formula as

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

s = (3 + 5 +6)/2 = 7

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

=> sqtr [ 7*(7-3)(7-5)(7-6)]

=> sqrt [7*4*2*1]

=> sqrt 56

The area of the triangle is sqrt 56

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We will use the formula of the area of a triangle given three sides.

The formula is the following:

A = sqrt( s*(s-a)(s-b)(s-c) such that s = perimeter/e , a, b, and c are the sides.

Let us calculate the perimeter.

==> P = 3+5+6 = 14

==> s = 14/2 = 7

==> Now we will substitute into A.

==> A = sqrt( 7*(7-3)*(7-5)*(7-6)

         = sqrt( 7*4*2*1) = sqrt56 = 7.48

Then, the area of the triangle is 7.48 square units.

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