Question

如下图，一个直角三角形中空白部分是一个正方形求阴影部分的面积

哈哈

Answer 1

解：由题意，易证△AED∽△DFB

得 AE:DF=DE:BF=AD:BD=12:18=2:3

设AE=2a则DE=DF=3a (CFDE为正方形)∴FB=（9/2）a

∵DE²+AE²=AD²  即（3a）²+ （2a）²=12²  a²=144/13

S阴影=0.5AE×DE+0.5DF×BF=0.5×2a ×3a +  0.5×3a ×（9/2）a=（39/4）a²

=（39/4）×(144/13)=108

Answer 2

两个红色的小直角三角形有个公共顶点，把斜边是12的小直角三角形绕这个公共顶点逆时针旋转90度。那么两个小直角三角形就合并成一个新的直角三角形，新的直角三角形的两条直角边分别是12和18。阴影部分面积就是12乘以18除以2。

Answer 3

解答：设直角△ABC，∠C=90°，正方形DCEF，边长=x，
AF=12，BF=18，D点在AC上，
设AD=a，则AC=a＋x，
设BE=b，则BC=b＋x，
由相似性得：DF／BC=AF／AB，
即①x／﹙b＋x﹚=12／30，∴b=﹙3／2﹚x，FE／AC=BF／AB，
即②x／﹙a＋x﹚=18／30，∴a=﹙2／3﹚x，
由勾股定理得：
③a²＋x²=12²解得：
x=36／√13，a=24／√13，
∴b=54／√13，
∴阴影面积=△ADF面积＋△FEB面积
=½ax＋½bx=½﹙a＋b﹚x
=½×﹙24／√13＋54／√13﹚×36／√13
=1304／13

Answer 4

你好，作文如下第一篇Final examinations end of the winter vacation started, I work with the teachers to return to the layout of the home. I think that winter vacation to do is work, play is to play, it is best to the Wangou assignments. But Mom and Dad said, assignments and play to cross, is part of the daily operations magical incantations to do. I had to do so. Therefore, my life is this winter vacation spent: assignments, watching television, playing and the New Year. Assignments, I am not consciously, the reminders to be Mom and Dad, I do. Operating do not have to ask Mom and Dad, they do not come, but empty, the teacher asked for back to school. Apart from a few do not operating was complete, most operations have been completed. Watching TV I like very much, if Mom and Dad do not ask me assignments, or not to turn off the TV, I really can see from the morning to get up at night. But his father said: TV to see long, the eyes influential. So, I actually only a part of cartoons and children's programs, as well as the Spring Festival evening party. Right, "Fuzhugege" I also secretly read several sets of very satisfied. I love playing, and her mother said that I would like to play. Winter vacation, Mom and Dad and I played table tennis, badminton played every game, I am prepared to give up the Wangou, they also had to accompany me, now think, I really too selfish. But my father said that I have great level of play increased. In addition, I also Guangguo shops, bought things, the time also miss the Spring Festival fireworks, extremely happy. New Year's is in the affirmative visited, I went to grandparents home, Waipojia and uncle's house, aunt home Baidoa New Year. New Year's time, fish and meat, I eat these things small, but eggs and steamed bread to eat a lot, eat a lot of sugar, peanuts and fruit, or a lot of red envelopes. In addition, the way could be with the sister, my brother playing, very happy. In short, this winter vacation, I live very happy, but also very full.

Answer 5

假象把DFB绕D点顺时针转，使DF和DE重合。
易知，三角形 ADB是直角三角形，
故阴影部分面积= 1/2*77*66=2541