As shown in the figure, in the trapezoidal ABCD, ab ∥ CD, ab = 3CD, diagonal lines AC and BD intersect at point O, and median lines EF intersect with AC and BD at two points m and N respectively, then the area of the shadow part in the figure is () A. 12B. 13C. 14D. 47

As shown in the figure, in the trapezoidal ABCD, ab ∥ CD, ab = 3CD, diagonal lines AC and BD intersect at point O, and median lines EF intersect with AC and BD at two points m and N respectively, then the area of the shadow part in the figure is () A. 12B. 13C. 14D. 47


Let DQ ⊥ AB pass through point D, intersect EF at a point W, ∵ EF is the median line of trapezoid, ∵ EF ∥ CD ∥ AB, DW = WQ, ∥ am = cm, BN = DN, ∥ EM = 12CD, NF = 12CD, ∥ EM = NF, ∥ AB = 3CD, let CD = x, ∥ AB = 3x, EF = 2x, ∥ Mn = ef - (EM + FN) = x, ∥ s △ ame + s △ BFN = 12 × EM × WQ + 12 ×



As shown in the figure, it is known that in △ ABC, ab = AC, CE is the middle line on the side of AB, extend AB to D, make BD = AB, connect CD


It is proved that: as shown in the figure, extend CE to f so that EF = CE, connect FB, ∵ CE is the middle line on the edge of AB, ∵ AE = be, and ∵ {bef =} AEC, ≌ △ bef, ≌ {FB = AC, ≌ 1 =} a, ∵ BD = AB,