平行四边形面积公式,关于对角线的,要推导过程.
人气:420 ℃ 时间:2019-10-17 07:59:27
解答
四边形两条边分别是a,b夹角α
S=(1/2absinα)*2=absinα
对角线c1,c2
a^2+b^2-2abcosα=c1^2
a^2+b^2-2abcos(180-α)=c2^2
a^2+b^2+2abcosα=c2^2
c2^2-c1^2=4abcosα
(c2^2-c1^2)/4=abcosα
(abcosα)^2+(absinα)^2=(ab)^2
((c2^2-c1^2)/4)^2+s^2=(ab)^2
s^2=(ab)^2-((c2^2-c1^2)/4)^2
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