HMMT 二月 2009 · GEN1 赛 · 第 3 题

HMMT February 2009 — GEN1 Round — Problem 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 the resulting trapezoid. 5 8

解析

[ 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 the resulting trapezoid. 5 8 Answer: 55 / 2 Solution: Drawing the perpendiculars from the point of intersection of the corners to the bases of the 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