三角形中的角（11岁及以上）
Angles in triangles (age 11+)
推导并运用三角形、平行四边形和梯形的面积公式，以及长方体和棱柱（包括圆柱）的体积公式，并将每个公式与其几何推理联系起来。
Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
学习证据 / Evidence
- 使用 A = ½(a + b) × h 计算梯形面积，并解释该公式为什么成立。
- 通过计算横截面积乘以长度来求出三棱柱的体积。
- 通过从棱柱公式出发进行推理，推导出圆柱的体积公式为 π × r² × h。
- Calculate the area of a trapezium using A = ½(a + b) × h and explain why the formula works
- Find the volume of a triangular prism by calculating cross-sectional area × length
- Derive the formula for the volume of a cylinder as π × r² × h by reasoning from the prism formula
评估问题 / Assessment
如果{{name}}需要铺设一块底边为4米、高为3米的三角形露台区域，他们能否算出面积，以知道需要买多少块瓷砖？
If {{name}} needs to tile a triangular section of a patio with a base of 4 m and height of 3 m, can they work out the area to know how many tiles to buy?