如图,Rt△ABC中,∠C=Rt∠,AC=8,BC=6,点D在边AC上,CD=0.5,过点D作DE⊥AB垂足为E,作A关

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  • Rt△ABC是边长比为3:4:5的直角三角形,所以按此比例计算即可

    AB = 10

    AD = 8 - 0.5 = 7.5 = 5份

    DE = 3份 = 4.5

    AE = 4份 = 6

    AA1 = 2AE = 12

    BA1 = 12 - 10 = 2

    点A1、F、D作为截点,由梅涅劳斯定理(不用定理作BG//AC交A1D于G)

    BA1/A1A * AD/DC * CF/FB = 1

    即 2/12 * 7.5/0.5 * CF/FB = 1

    CF/FB = 2/5

    CF = BC*2/7 = 12/7

    四边形DEBF的面积 = S△ABC - S△CDF - S△AED

    = 6*8/2 - 0.5*12/7*1/2 - 6*4.5/2

    = 24 - 3/7 - 27/2

    = 141/14