已知三棱柱的底面为正三角形,侧面是全等的矩形
侧面是全等矩形只能是正三棱柱,相当于正三角形里面内切一个半径为R的圆可算出一边长L=2Rtan(π/3) 周长就是3L=6Rtan(π/3)=6√3R
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绛旓細濡傚浘锛宸茬煡涓夋１鏌 鐨勫簳闈㈡槸姝ｄ笁瑙掑舰锛渚ч潰 鏄煩褰紝 鍒嗗埆涓 鐨勪腑鐐癸紝 涓 涓婁竴鐐癸紝杩 鍜 鐨勫钩闈氦 浜 锛屼氦 浜 .锛1锛夎瘉鏄庘埗 , 涓斿钩闈 骞抽潰 ;锛2锛夎 涓 鐨勪腑蹇. 鑻 // 骞抽潰 ,涓 锛屾眰鐩寸嚎 涓庡钩闈 鎵鎴愯鐨勬寮﹀....
绛旓細锛1锛妫辨煴渚ф１閮界浉绛,渚ч潰鏄钩琛屽洓杈瑰舰锛涘鏋搴曢潰涓烘涓夎褰,鍒欎笁涓晶闈竴瀹氱浉鍚.锛2锛変晶闈㈤兘鏄彵褰,涓斿繀椤讳负骞宠鍥涜竟褰,閭ｈ繖浜涜彵褰㈤兘鏄鏂瑰舰.妫辨煴鐨勪晶妫遍兘鐩哥瓑,鎵浠ヨ繖浜涜彵褰㈤兘鏄畬鍏ㄧ浉鍚岀殑姝ｆ柟褰.
绛旓細鐢遍鎰忕煡锛屾涓夋１鏌变负姝ｄ笁妫辨煴锛岀敱涓夎鍥惧緱搴曢潰涓夎褰杈归暱涓4锛屾１鏌辩殑楂樹负2锛屸埓妫辨煴鐨勪綋绉疺=12脳4脳4脳32脳2=83锛庢晠绛旀鏄細83锛
绛旓細渚ч潰鏄叏绛夌煩褰㈠彧鑳芥槸姝ｄ笁妫辨煴,鐩稿綋浜姝ｄ笁瑙掑舰閲岄潰鍐呭垏涓涓崐寰勪负R鐨勫渾 鍙畻鍑轰竴杈归暱L=2Rtan(蟺/3) 鍛ㄩ暱灏辨槸3L=6Rtan(蟺/3)=6鈭3R
绛旓細HD鍦ㄥ钩闈'DB鍐呫鎵浠'E骞宠骞抽潰C'DB 锛2锛夊洜涓篈鈥楨鏄涓夎褰A'B'C'鐨勪腑鐐,鎵浠 A'E鍨傜洿B'C'鍥犱负abc-a'b'c'鏄 姝涓夋１鏌 鎵浠 AA'鍨傜洿搴曢潰 鎵浠A'鍨傜洿A'E 鎵浠ュ钩琛屽洓杈瑰舰AA'EF鏄煩褰 鎵浠 A'E鍨傜洿EF 鍥犱负 鐩寸嚎EF銆丅'C'鍦ㄤ负骞抽潰BB'C'C鍐呯殑涓ゆ潯鐩镐氦鐩寸嚎, 涓 A'E涓庡畠浠...
绛旓細杩炴帴OD锛屽垯OD涓 涓 杈逛笂鐨勪腑浣嶇嚎锛屾墍浠 .鍙 骞抽潰ABD锛 骞抽潰ABD锛屾墍浠 骞抽潰ABD.锛堚叀锛夊洜涓 涓虹瓑杈逛笁瑙掑舰锛D涓篈C涓偣锛屾墍浠 锛岀敱渚ф１鍨傜洿浜搴曢潰鐭ワ紝涓夋１鏌涓虹洿涓夋１鏌憋紝鎵浠ュ钩闈 骞抽潰 .鍙堝钩闈BC 骞抽潰 =AC锛孊D 骞抽潰ABC锛屾墍浠D 骞抽潰 锛屽張AD 骞抽潰 锛 骞抽潰 锛...
绛旓細杩炵粨 锛 锛 锛 锛庡垯 锛 鈭 涓 鎵鎴愮殑瑙掑嵆涓 涓 鎵鎴愮殑瑙 锛屸埖 鏄涓夋１鏌锛屼笖鍚勬１闀垮潎涓 锛屸埓 锛 锛屸埓鈻 涓烘涓夎褰紝鏁 锛屽嵆寮傞潰鐩寸嚎 涓 鎵鎴愮殑瑙掍负 锛 锛2锛夌敱锛1锛夌煡锛 锛 锛3锛 锛屸埓鐐 鍒板钩闈 鐨勮窛绂伙紝鍗充负鐩寸嚎 鍒板钩闈 鐨勮窛绂...
绛旓細C 璇曢鍒嗘瀽锛氭涓夋１鏌涓烘涓夋１鏌憋紝浣撶Н涓 鐨勭悆浣撳崐寰勪负 锛岀敱姝ゅ彲浠ュ緱鍒涓夋１鏌辩殑楂樹负 锛搴曢潰姝ｄ笁瑙掑舰涓績鍒颁笁瑙掑舰杈圭殑璺濈涓 锛屾晠鍙緱鍒颁笁瑙掑舰鐨勯珮鏄 锛屼笁瑙掑舰杈归暱鏄 锛屾墍浠ヤ笁妫辨煴鐨勮〃闈㈢Н涓 .
绛旓細鍥犱负搴曢潰鏄涓夎褰 鑰岀悆鍐呭垏涓夋１鏌 鍗虫涓夎褰㈠唴鍒囩殑鐞冨崐寰勪篃涓篟 鏍规嵁姝ｄ笁瑙掑舰涓夌嚎鍚堜竴 R=1/3楂 璁捐竟闀夸负a 鏍瑰彿3/2*a*1/3=R a=2鏍瑰彿3*R
