已知四面体ABCD中,AB=CD=根号13,BC=AD=二倍根号5,BD=AC=5,求四面体ABCD的体积
已知四面体ABCD中,AB=CD=根号13,BC=AD=二倍根号5,BD=AC=5,求四面体ABCD的体积
数学人气:620 ℃时间:2019-09-21 06:47:02
优质解答
补成长方体AEBF-GCHD,注意这里的顶点字母之间的对应.设这个长方体的长为a,宽为b,高为c,则a^2+b^2=13,b^2+c^2=20,a^2+c^2=25.解得:a=3,b=2,c=4,∴四面体ABCD的体积=3×2×4÷6=4(体积单位)
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