Difference between revisions of "1983 AIME Problems/Problem 11"
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== Problem == | == Problem == | ||
The solid shown has a square base of side length <math>s</math>. The upper edge is parallel to the base and has length <math>2s</math>. All edges have length <math>s</math>. Given that <math>s=6\sqrt{2}</math>, what is the volume of the solid? | The solid shown has a square base of side length <math>s</math>. The upper edge is parallel to the base and has length <math>2s</math>. All edges have length <math>s</math>. Given that <math>s=6\sqrt{2}</math>, what is the volume of the solid? | ||
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== Solution == | == Solution == |
Revision as of 02:40, 21 January 2007
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 .