How do you use Heron's formula to find the area of a triangle with sides of lengths #6 #, #4 #, and #8 #?

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Answer 1 · 2016-02-15T19:27:26

Heron's formula uses the lengths of the sides and the semiperimeter to find the area of a triangle

The formula is given as #sqrt((s)(s-a)(s-b)(s-c))#

Where #s = (a + b + c)/2#

With this information, it should be easy to plug in the numbers to find the area

First, find s

#(6 + 4+8) / 2# =====> #s = 9#

Now plug this into Heron's formula

#sqrt((9)(9-6)(9-4)(9-8))#

#sqrt((9)(3)(5)(1))#

#sqrt(135)#

This cannot be simplified any furthur. So we are done.