三至五年级Geometry & Topology课程已上线
Area, perimeter and angles
Area as the number of unit squares that cover a shape, perimeter as the distance around it, area of rectangles, first volumes, and angles as amounts of turn measured in degrees.
math.geom.area-angles
前置知识
6 项必需的前置知识（一直追溯到底）
你将学会
- Find areas by counting unit squares and by multiplying length by width, and compute perimeters.
- Show that shapes with the same perimeter can have different areas, and vice versa.
- Measure and draw angles in degrees, and classify triangles and quadrilaterals by their sides and angles.
- Find the volume of a rectangular box by counting unit cubes.
定义
- Area is the amount of surface a shape covers, measured in square units.
- Perimeter is the total length of the boundary of a shape.
- An angle is the amount of turn between two rays from a common point; a full turn is 360°.
定理
- The area of a rectangle is length × width.
- The angles of a triangle in the plane add up to 180°.
- The volume of a rectangular box is length × width × height.
常见误解
- Confusing area with perimeter.
- Thinking an angle gets bigger when its arms are drawn longer.
- Believing that shapes with equal perimeters must have equal areas.
通向
可选发现
- Measure theory and integration Which sets of points have an area at all? Measure theory answers this; with the axiom of choice, some sets cannot be given a countably additive area that is unchanged by sliding them.
学习路径
延伸阅读
- Paul Lockhart, Measurement (2012) — For teachers and curious adults.