Difference between revisions of "1983 AIME Problems/Problem 11"
(wik, asymptote needed (will do later)) |
I like pie (talk | contribs) m |
||
Line 4: | Line 4: | ||
</asy></center> -->[[Category:Asymptote needed]] | </asy></center> -->[[Category:Asymptote needed]] | ||
+ | |||
[[Image:1983Number11.JPG]] | [[Image:1983Number11.JPG]] | ||
== Solution == | == Solution == |
Revision as of 12:13, 25 April 2008
Problem
The solid shown has a square base of side length . The upper edge is parallel to the base and has length . All edges have length . Given that , what is the volume of the solid?
Solution
First, we find the height of the figure by drawing a perpendicular from the midpoint of to . The hypotenuse of the triangle is the median of equilateral triangle one of the legs is . We apply the Pythagorean Theorem to find that the height is equal to .
Next, we complete the figure into a triangular prism, and find the area, which is .
Now, we subtract off the two extra pyramids that we included, whose combined area is .
Thus, our answer is .
See also
1983 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |