Find the area of the triangle with the given vertices.
$A ( - 3 , - 4 , - 9 ) , B ( - 7 , - 9 , - 1 ) , C ( 8,8,6 )$
A) $\sqrt { 6399.25 }$ square units
B) $\sqrt { 3199.63 }$ square units
C) $\sqrt { 12798.50 }$ square units
D) $\sqrt { 25597.00 }$ square units
E) $\sqrt { 51194.00 }$ square units

Question

Find the area of the triangle with the given vertices.
 $A ( - 3 , - 4 , - 9 ) , B ( - 7 , - 9 , - 1 ) , C ( 8,8,6 )$ 
A) $\sqrt { 6399.25 }$ square units
B) $\sqrt { 3199.63 }$ square units
C) $\sqrt { 12798.50 }$ square units
D) $\sqrt { 25597.00 }$ square units
E) $\sqrt { 51194.00 }$ square units

Quizplus · Accepted Answer

The area of a triangle with vertices in 3D can be found using the cross product of vectors AB and AC. The magnitude of the cross product gives twice the area of the triangle. After calculating the vectors and their cross product, the magnitude squared is 12798.50, so the area is $\sqrt{12798.50}$.

Find the Area of the Triangle with the Given Vertices A(−3,−4,−9),B(−7,−9,−1),C(8,8,6)A ( - 3 , - 4 , - 9 ) , B ( - 7 , - 9 , - 1 ) , C ( 8,8,6 )A(−3,−4,−9),B(−7,−9,−1),C(8,8,6)

Find the Area of the Triangle with the Given Vertices $A ( - 3 , - 4 , - 9 ) , B ( - 7 , - 9 , - 1 ) , C ( 8,8,6 )$