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~~4.683735144.6837

Explanation:

Heron's formula states that, given a triangle with side lengths a, b, ca,b,c and semiperimeter s = (a+b+c)/2s=a+b+c2 the area AA of the triangle is

A= sqrt(s(s-a)(s-b)(s-c))A=s(sa)(sb)(sc)

In this case, we have a = 2a=2, b = 6b=6, and c = 5c=5. Then, for this triangle we have s = (2+6+5)/2 = 13/2s=2+6+52=132. Applying Heron's formula gives us

A = sqrt(13/2(13/2-2)(13/2-6)(13/2-5))A=132(1322)(1326)(1325)

=sqrt(13/2*9/2*1/2*3/2)=132921232

=sqrt(351/16)=35116

=sqrt(351)/4~~4.6837=35144.6837