How do you use Heron's formula to find the area of a triangle with sides of lengths #18 #, #9 #, and #13 #?

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Answer 1 · 2016-02-22T01:36:08

Heron's formula relates the area of a triangle to the side of the triangle

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

Where s is the sum of the side lengths divided by 2.

So, first we find s, the semiperimeter

#18+9+13/2 = 20#

So #s=20#

Now we simply plug in the values into Heron's formula

#A = sqrt((20)(20-18)(20-9)(20-13))#

#A = sqrt((20)(2)(11)(7))#

#A = sqrt(3080)#

#A = 2sqrt(770)#

which is approximately 55.5