✔ 最佳答案
圖片參考:
https://s.yimg.com/rk/HA00981853/o/161821642.png
sin60° = AN/12
AN = 12sin60° cm
∵M為ΔABC的形心
∴AM = (2/3)*12sin60°
= 8sin60° cm
圖片參考:
https://s.yimg.com/rk/HA00981853/o/1163249243.png
在ΔADM,
正四面體的高DM = √[12²-(8sin60°)²]
= √96 cm
正四面體的體積 = (1/3) * (1/2)(12)(12)*sin60° * √96
≈ 203.647
= 204 cm³ (取三位有效數字)
2015-04-19 22:33:22 補充:
這裏有條公式:
http://mathseasy.hk/articles/tetrahedron/
正四面體的高 = √(2/3)*邊長
∴正四面體的體積 = (1/3) * (1/2)(12)(12)*sin60° * √(2/3)*12
= 204 cm³ (取三位有效數字)