# Mary Evans Picture Library. Historical archive. Images of history. Pictures

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Area Formulas: Triangle, Parallelogram, Trapezoid
To begin this lesson, click the ‘Create a random triangle’ button below; then, repeatedly click the other button. Do it again and again and again—make sure you understand what is meant by base/height pairs in a triangle. (The triangles are randomly-generated, so you might see some ‘unsatisfying’ situations, like really skinny triangles!) A precise discussion of base/height pairs follows this JSXGraph exploration. Please click the 'Create a random triangle' button above to explore base/height pairs in a triangle Take a vertex of a triangle, and drop a segment that is perpendicular to the opposite side (first picture below) or (if needed) to an extension of the opposite side (second picture below). The segment just created is called a height or altitude of the triangle, and the side opposite this vertex is called the corresponding base. Since every triangle has three vertices, every triangle has three base/height pairs. Let and denote a base/height pair for a triangle.

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