格点多边形的面积（课件）-2026-2027学年人教版五年级上册数学

格点多边形的面积人教版五年级上册数学我同学们，这是我们熟悉的方格纸。如果我把横线和竖线都擦去，只保留交叉点，会变成什么样？·

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································把线擦去，只留交点格点图方格纸你知道格点多边形吗？顶点都在格点上的多边形可以是不规则形状想一想：怎么计算格点多边形的面积？割补法学习任务一先独立思考，再小组讨论。（1）怎么使用分割法计算面积？分割成几部分？（2）怎么使用添补法计算面积？添补成什么图形？·

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···························格点多边形把它分割成若干个基本图形，分别计算面积后相加。方法一：分割法·

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···························格点多边形2×3÷2+1×3÷2+(2+3)×1÷2+(2+3)×3÷2=3+1.5+2.5+7.5=14.5把多边形补成一个大长方形，用大长方形的面积减去添补上的空白部分的面积。方法二：添补法·

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··························格点多边形4×6-2×3÷2-1×3÷2-3×2÷2-4×1÷2=24-3-1.5-3-2=14.5还有一种巧妙的方法可以计算格点多边形的面积。············································································································································································································①②③④内部格点——用a

表示；边界格点——用b

表示。············································································································································································································学习任务二小组合作填表图形内部格点数

a边界格点数

b面积

S（割补法）a+b÷2-1①

②

③

④

①②③④图形内部格点数

a边界格点数

b面积

S（割补法）a+b÷2-1①

24

3

②2

7

4.5

③5

10

9

④12

13

17.5你有什么发现？比较：同一图形的a、b、S之间有什么关系？

计算验证：计算a+b÷2−1，看是否等于S。图形内部格点数

a边界格点数

b面积

S（割补法）a+b÷2-1①

24

3

3②2

7

4.5

4.5③5

10

9

9

④12

13

17.517.5格点多边形面积S=a+b÷2−1图形内部格点数

a边界格点数

b面积

S（割补法）a+b÷2-1①

24

3

3②2

7

4.5

4.5③5

10

9

9

④12

13

17.517.5格点多边形面积S=a+b÷2−1这个方法于1899年由奥地利数学家皮克证明，因此被称为皮克定理（Pick'sTheorem）。通过本节课的学习，你有什么收获