What is the area of a triangle with sides of length 2, 6, and 5?

1 Answer
Mar 14, 2016

Apply Heron's formula to find the area to be

sqrt(351)/4~~4.6837

Explanation:

Heron's formula states that, given a triangle with side lengths a, b, c and semiperimeter s = (a+b+c)/2 the area A of the triangle is

A= sqrt(s(s-a)(s-b)(s-c))

In this case, we have a = 2, b = 6, and c = 5. Then, for this triangle we have s = (2+6+5)/2 = 13/2. Applying Heron's formula gives us

A = sqrt(13/2(13/2-2)(13/2-6)(13/2-5))

=sqrt(13/2*9/2*1/2*3/2)

=sqrt(351/16)

=sqrt(351)/4~~4.6837