Triangle in Three Dimensions

Calculate the area of triangle ABC with the following vertices: A(1,3,0), B(0,2,5), and C(\textrm{-}1,0,2).
Source: NCTM Mathematics Teacher, February 2006

Apply the distance formula in three dimensions
Apply Heron’s formula for the area of a triangle ABC with side lengths a,b,c
area =\sqrt{s(s-a)(s-b)(s-c)} where s=1/2(a+b+c)
area =\sqrt{6.53(6.53-\sqrt{27})(6.53-\sqrt{17})(6.53-\sqrt{14})}

Answer: 7.64 square units


About mvtrinh

Retired high school math teacher.
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