What is the area of the parallelogram with vertices A(1,5,0), B(6,10,−3), C(−4,5,−2), and D(1,10,−5)?
1 Answer
Explanation:
First we should verify that the 4 points really are coplanar. Following, for instance, the method described in:
Equation of a Plane determined by 3 points
I checked it obtaining the plane defined by the points A, B and C, then trying D in the equation of the plane, verifying that these 4 points are indeed coplanar.
Further: note that the figure ABCD is composed of the triangles ABC and ACD.
Repeating the coordinates of the points:
A(1,5,0)
B(6,10,-3)
C(-4,5,-2)
D(1,10,-5)
Obtaining sides of the triangles ABC and ACD:
Just a minute!
Since
Using Heron's Formula
Triangle ABC (
Other way to find the area of the kind of triangle involved in this question is described in:
when the triangle is embedded in three-dimensional space