梯形ABCD的面积是多少平方厘米

  • 时间:2020-05-16 11:04:24
  • 分类:数学世界
  • 阅读:133 次

数学题:在直角梯形ABCD中,AB=15厘米,AD=12厘米,阴影部分的面积为15平方厘米,梯形ABCD的面积是多少平方厘米?

直角梯形

数学题解答:此题需要添加一条辅助线,连接AE,阴影三角形面积与三角形AEF相等。根据阴影三角形面积是15平方厘米,所以三角形AEF面积也是15平方厘米。三角形AEF的底是EF,则高是AB=15厘米,据此可以算出EF的长度:

EF=15×2÷15=2(厘米)

所以BF=12-2=10(厘米)

由于阴影三角形与三角形BEC的高相同,所以面积之比就是它们底的比,设BEC面积为X平方厘米,则有:

10:15=12:X

X=18

直角梯形的面积是:15×12+18=198(平方厘米)

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