Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Tetrahedron.
Tetrahedron Problem – AIME I, 1992
Faces ABC and BCD of tetrahedron ABCD meet at an angle of 30,The area of face ABC=120, the area of face BCD is 80, BC=10. Find volume of tetrahedron.
- is 107
- is 320
- is 840
- cannot be determined from the given information
Key Concepts
Area
Volume
Tetrahedron
Check the Answer
Answer: is 320.
AIME I, 1992, Question 6
Coordinate Geometry by Loney
Try with Hints
Area BCD=80=\(\frac{1}{2} \times {10} \times {16}\),
where the perpendicular from D to BC has length 16.

The perpendicular from D to ABC is 16sin30=8
[ since sin30=\(\frac{perpendicular}{hypotenuse}\) then height = perpendicular=hypotenuse \(\times\) sin30 ]
or, Volume=\(\frac{1}{3} \times 8 \times 120\)=320.
Other useful links
- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA