1 . 武汉大学附属中学实验楼一侧有块扇形空地,如图,经测量其半径为
,圆心角为
.学校准备在此扇形空地上修建一处高一年级青少年科学院室外活动露天教室,现有两个设计方案面向全体高一年级学生征求意见:
方案一:按如下方式修建一平行四边形“创意型(
)”教室,其余空地绿化(如下左图):在弧
上任取一点
(异于
),过点
分别作
、
平行于
、
,交
、
分别于
、
两点;
方案二:按如下方式修建一矩形“传统型(
)”教室,其余空地绿化(如下左图):在弧
上任取一点
(异于
,
),过点
分别作
垂直于
,
平行于
,分别交
、
于
、
两点.经随机走访调查,对于这两种方案主要有二种反馈意见:
说法一:方案一教室形状有创意,感觉教室面积更大,所以方案一好;
说法二:方案二传统矩形教室感觉亲切,面积更大,所以方案二好;
说法三:只要点
(异于
,
)固定,按照这两个方案修建的教室面积完全一样,所以就教室面积大小而言,这两个方案没区别.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/e868dba3-a61a-4d7a-9790-3487d636e6f4.png?resizew=198)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7b0c30c3-db1b-400d-aa2c-ffa709de90b1.png?resizew=191)
(1)亲爱的高一学子,根据所学,你认为说法三对吗?(只需作出判断,无需说明理由);
(2)请大家在这两个方案里面,选择一个你最喜欢的方案,并根据你选择的方案求出教室面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f5c1c5015c71722cff00a02ad27a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
方案一:按如下方式修建一平行四边形“创意型(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033274547930b2e2dcd4ea4919a36738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
方案二:按如下方式修建一矩形“传统型(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9e7f4b57507c84003d2a9d6916c540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
说法一:方案一教室形状有创意,感觉教室面积更大,所以方案一好;
说法二:方案二传统矩形教室感觉亲切,面积更大,所以方案二好;
说法三:只要点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/e868dba3-a61a-4d7a-9790-3487d636e6f4.png?resizew=198)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/7b0c30c3-db1b-400d-aa2c-ffa709de90b1.png?resizew=191)
(1)亲爱的高一学子,根据所学,你认为说法三对吗?(只需作出判断,无需说明理由);
(2)请大家在这两个方案里面,选择一个你最喜欢的方案,并根据你选择的方案求出教室面积的最大值.
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