1984 AIME Problems/Problem 9
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Problem
In tetrahedron 
, edge 
has length 3 cm. The area of face 
is 
and the area of face 
is 
. These two faces meet each other at a 
angle. Find the volume of the tetrahedron in 
.
Solution
For non-asymptote version of image, see Image:1984_AIME-9.png.Position face on the bottom. Since ![[\triangle ABD] = 12 = \frac{1}{2} \cdot AB \cdot h_{ABD}](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/1/2/b/12b1a5a21ec9912ae821a28de0609bbad7cdf1c2.gif)
, we find that 
. The height of forms a 
with the height of the tetrahedron, so 
. The volume of the tetrahedron is thus 
.
See also
| 1984 AIME (Problems • Resources) | ||
| Preceded by Problem 8 | Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
