HMMT 二月 2009 · GEN1 赛 · 第 3 题

英文解析

3. [ 3 ] A rectangular piece of paper with side lengths 5 by 8 is folded along the dashed lines shown below,
   so that the folded flaps just touch at the corners as shown by the dotted lines. Find the area of theresulting trapezoid.
   Answer: 55 / 285
   Solution: Drawing the perpendiculars from the point of intersection of the corners to the bases ofthe trapezoid, we see that we have similar 3 − 4 − 5 right triangles, and we can calculate that the length
   8+3
   of the smaller base is 3. Thus the area of the trapezoid is · 5 = 55 / 2. 2