📚 Area of Triangles | 三角形的面积
Triangles are one of the most important shapes in geometry, and finding their area is a skill you will use again and again, from simple diagrams to IGCSE exam problems. In this guide, we will build a complete understanding of the area of a triangle: where the formula comes from, how to apply it, and how to avoid the traps that cause students to lose marks.
三角形是几何学中最重要的图形之一，计算其面积是你反复使用的技能，从简单图形到 IGCSE 考试题目都会用到。在本指南中，我们将完整理解三角形的面积：公式从哪里来、如何应用，以及如何避免导致失分的陷阱。
1. Triangle Basics | 三角形的基础知识
A triangle is a three-sided polygon with three vertices and three interior angles. The sum of the three interior angles is always 180°. This fact is useful in many area problems because it helps us confirm whether a triangle is right-angled, acute, or obtuse.
三角形是有三条边、三个顶点和三个内角的多边形。三个内角的和恒为 180°。这个性质在许多面积问题中都很有用，因为它帮助我们判断三角形是直角、锐角还是钝角三角形。
Every triangle has three sides, and each side can pair with a height that is perpendicular to it. This flexibility is important: the same triangle has three different valid base-height pairs, and we may choose any one to find its area, as long as the chosen height is truly perpendicular to the chosen base.
每个三角形都有三条边，每条边都可以搭配一条与它垂直的高。这种灵活性很重要：同一个三角形有三组不同的底高对应，我们可以任选一组来计算面积，前提是所选高确实垂直于所选底边。
Triangles are often classified by their angles:
三角形常按角分类：
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Acute triangle: all three angles are less than 90°.
锐角三角形：三个内角都小于 90°。
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