Problem:
Let points A=(0,0,0),B=(1,0,0),C=(0,2,0), and D=(0,0,3). Points E, F,G, and H are midpoints of line segments BD,AB,AC, and DC respectively. What is the area of EFGH?
Answer Choices:
A. 2
B. 325
C. 435
D. 3
E. 327
Solution:
The midpoint formula gives E=(21,0,23),F=(21,0,0),G=(0,1,0), and H=(0,1,23). Note that EF=GH=23,EF⊥EH,GF⊥GH, and
EH=FG=(21)2+12=25.
Therefore EFGH is a rectangle with area 23⋅25=(C)435.
