Explore Triangle Area and Height

① This interactive GeoGebra activity lets students explore the area of different triangles by dragging vertices, and understand that the height is the perpendicular segment from a vertex to the opposite side (or its extension). ② Core math concepts include the triangle area formula (Area = base × height ÷ 2), the definition of altitude/height, perpendicularity, and how changing vertex positions affects the area while the base remains fixed. ③ Construction details: The triangle ABC is built using the Polygon command; lines through vertices perpendicular to opposite sides are created with Line and OrthogonalLine; Intersect finds the foot of the perpendicular; Segment draws the altitude; Angle marks the right angle; text objects display side lengths and area values dynamically. ④ Suitable for middle school geometry classes or upper elementary enrichment, this activity serves as a hands-on investigation to reinforce the concept that height must be perpendicular to the base and to verify the area formula across various triangle shapes.