题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120106-29605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120106-78363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120107-29646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120106-78363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120107-79589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120107-10846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120107-42323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120108-70723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120108-44748.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120108-83673.png)
解析
则上底长为btan∠AOB,下底长为atan∠AOB,
∴Sn=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120108-52285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120108-52285.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-55396.png)
又∵梯形1距离点O的距离a=1,b=3,
∴S1=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-55396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-10455.png)
第2009个梯形前面已有2008×2个奇数,
2009个梯形上底距点O的距离为第2008×2+1个奇数,
下底为第2008×2+2个奇数,
∴第2009个梯形的两边长分别为:
a=2×(2008×2+1)-1=8033,
b=2×(2008×2+1)+1=8035,
故S2009=
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-55396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-90352.png)
故答案为
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-10455.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120109-90352.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120102-84094.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120102-47327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120103-10056.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120053-73935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120053-26648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120054-81452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120054-41070.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120054-46842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120054-18954.png)
猜想、推理知:当
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120055-36250.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120055-58840.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120055-73519.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120047-54300.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120038-61542.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120038-93318.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120038-25321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120038-25321.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120039-43895.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120039-16888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120039-16888.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120039-54543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120040-88471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120040-88471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120040-51310.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120040-54152.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120040-14492.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120041-61072.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120041-79475.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120041-18843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120042-79406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191104/20191104120031-68139.png)
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