Triangle with Given Area

① This example demonstrates how to dynamically construct a triangle with a fixed given area in GeoGebra, using random elements and button interactions to generate different shapes while keeping the area constant. ② The core mathematical concept is the triangle area formula (base × height / 2) and the invariance of area under geometric variation, involving random experiments and function graph visualization. ③ Construction details: Sequence generates point lists, Polygon builds the triangle, RandomElement selects random vertices, If controls the area condition, a button (button1) triggers random updates, text objects (text1, text2) display the area value, and sliders/parameters (a, b, d, c, e) adjust the base and height. ④ Suitable for middle school geometry teaching, to intuitively understand the area formula, random experiments, and dynamic geometric interaction, and to explore multiple forms of equal-area triangles.