How do you use Heron's formula to find the area of a triangle with sides of lengths #19 #, #14 #, and #13 #?

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Answer 1 · 2016-02-04T00:57:50

The area of the triangle would be #55.3 units^2#

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First we would find S which is the sum of the 3 sides divided by 2.

#S = (19 + 14 + 13)/2 # = #46/2# = #23#

Then use Heron's Equation to calculate the area.

#Area = sqrt(S(S-A)(S-B)(S-C)) #

#Area = sqrt(23(23-19)(23-14)(23-13)) #

#Area = sqrt(8.5(4)(9)(10)) #

#Area = sqrt(3060) #

#Area = 55.3 units^2 #