Solution.
We can use Heron formula which states
The area of a triangle with sides a,b,c is equal to
S=p(p−a)(p−b)(p−c)
where p=2a+b+c.
Using the formula to find the distance between two points A(x1,x2,x3),B(y1,y2,y3)
which is
AB=(x1−y1)2+(x2−y2)2+(x3−y3)2
we can calculate the length of sides between the three points given
let say A(5,3,2), B(-2,7,-1) and C(4,-2,6).
After that, we substitute to Heron formula.
AB=(5+2)2+(3−7)2+(2+1)2=49+16+9=74.BC=(−2−4)2+(7+2)2+(−1−6)2=36+81+49=166.AC=(5−4)2+(3+2)2+(2−6)2=1+25+16=42.p=2a+b+c=21(8.6+12.88+6.48)=13.98S=(13.98)(13.98−8.6)(13.98−12.88)(13.98−6.48)=24.9square unitsAnswer. 24.9 square units.
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