正四棱锥S-ABCD底面边长为a 连接AC,AC=(√2)a 做CE⊥SB ,连接AE,则AE⊥SB ===>∠AEC=120° AC中点0 ,连接OE,EO⊥AC且平分∠AEC ===>OE =OAtan30°=(√6)a/6 0B=(√2)a/2 ==>sin∠SBO =(√3)/3 ==>tan∠SOB =(√2)/2 高SO =0Btan∠SOB =a/2 侧棱SB =0B/sin∠SOB =(√6)a/2 做SF⊥BC于F.连接0F,在直角三角形SOF中 斜高SF =(√2)a/2
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