设DE=x,
∵DF ⊥AC,DE⊥BC
∴△ADF∽△DBE
BE/DF=4/6
∴BE=2/3x
∴BC=5/3x
同理.AC=5/2x
(5/3x)^2+(5/2x)^2=AD^2=100
∴13x^2=144
△BDE 的面积=1/2×x×2/3x=1/3x^2
△ADF的面积=1/2×x×3/2x=3/4x^2
∴阴影面积=1/3x^2+3/4x^2=13/12x^2=144×1/12=12