Question

完整过程，谢谢！

Answer 1

设 CD = a，HG = h， 则，AB = 3a

梯形ABCD面积 = （a + 3a）h/ 2 = 2ah

△OAB ∽ △OCD

OH：OG = CD：AB = 1:3

OH：HG = 1:4

OH = h/4

OJ = HJ - OH = h/2 - h/4 = h/4

△AEM ∽ △ADC

EM = CD/2 = a/2

△BFN ∽ △BCD

FN = CD/2 = a/2

EF = (AB + CD)/2 = 2a

MN = EF = EM - FN = a

S△AEM = S△BFN = 1/2 * a/2 * h/2 = ah/8

S△OCD = S△OMN = 1/2 * a * h/4 = ah/8

S阴影 =S△AEM + S△BFNS + △OCD + S△OMN

= ah/2

S阴影 / S梯形ABCD = (ah/2) / (2ah) = 1/4

Answer 2

1/4

Answer 3

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Answer 4

姐姐