GWD 2-30

In the figure, each side of square ABCD has length 1, the length of line segment CE is 1, and the length of line segment BE is equal to the length of line segment DE.  What is the area of the triangular region BCE?

我也选的C

可是答案是B..

平面几何：答案就是B

立体几何：答案可以是C，但也可以是B，甚至可以是别的解

因此很明显，本题是B

想复杂了...看到那个图就按立体几何想的

Let the extention of CE touches BD, and call that point F, since BE = DE, and BC = CD, then the extention of CE (EF) must be the height of trangle BED

Thus the area of BCE = the area of BFE - the area of BFC

Since ABCD is a square with each side's length equals 1, CF = Ö2/2, and the area of BCF = Ö2/2 * Ö2/2 / 2 = 1/4，

Since CE 1 and CF = Ö2/2, then EF = 1 + Ö2/2, the area of BEF = (1 + Ö2/2) * Ö2/2 / 2 = (1 + Ö2)/4

Thus the area of BCE = (1 + Ö2)/4 - 1/4 = Ö2/4, which is B