Difference between revisions of "2022 AMC 8 Problems/Problem 24"
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Solution by aops-g5-gethsemanea2 | Solution by aops-g5-gethsemanea2 | ||
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It is easy to visualize the prism when <math>\triangle BJG</math> is the base and <math>\overline{\rm AB}</math> is the height. | It is easy to visualize the prism when <math>\triangle BJG</math> is the base and <math>\overline{\rm AB}</math> is the height. |
Revision as of 20:47, 28 January 2022
Contents
Problem
The figure below shows a polygon , consisting of rectangles and right triangles. When cut out and folded on the dotted lines, the polygon forms a triangular prism. Suppose that
and
. What is the volume of the prism?
Solution
While imagining the folding, goes on
goes on
and
goes on
So,
and
Also,
becomes an edge parallel to
so that means
Since then
So, the area of
is
If we let
be the base, then the height is
So, the volume is
Solution by aops-g5-gethsemanea2
Remark
It is easy to visualize the prism when is the base and
is the height.
~MathFun1000
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.