2012 AMC 10A Problems/Problem 21
Problem
Let points =
,
=
,
=
, and
=
. Points
,
,
, and
are midpoints of line segments
and
respectively. What is the area of
?
Solution
Consider a tetrahedron with vertices at on the
-plane. The length of
is just one-half of
because it is the midsegment of
The same concept applies to the other side lengths.
and
. Then
and
. The line segments lie on perpendicular planes so quadrilateral
is a rectangle. The area is
See Also
2012 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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All AMC 10 Problems and Solutions |