2025 AMC 12A Problems/Problem 20: Difference between revisions
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==See Also== | ==See Also== | ||
{{AMC12 box|year=2025|ab=A|before=[[ | {{AMC12 box|year=2025|ab=A|before=[[2025 AMC 12A Problems/Problem 19]]|after=[[2025 AMC 12A Problems/Problem 21]]}} | ||
* [[AMC 12]] | * [[AMC 12]] | ||
* [[AMC 12 Problems and Solutions]] | * [[AMC 12 Problems and Solutions]] | ||
Revision as of 16:58, 6 November 2025
Problem
The base of the pentahedron shown below is a 
rectangle, and its lateral faces are two isosceles triangles with base of length 
and congruent sides of length 
, and two isosceles trapezoids with bases of length 
and and nonparallel sides of length .
[Diagram]
What is the volume of the pentahedron?
Solution 1 (Split Into Three Parts)
Notice that the triangular faces have a slant height of 
and that the height is therefore 
. Then we can split the pentahedron into a triangular prism and two pyramids. The pyramids each have a volume of 
and the prism has a volume of 
. Thus the answer is 
~ Shadowleafy
See Also
| 2025 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by 2025 AMC 12A Problems/Problem 19 |
Followed by 2025 AMC 12A Problems/Problem 21 |
| 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 AMC 12 Problems and Solutions | |
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