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area of a hexagon Proposition 34 represents a natural starting point for our investigation of the emergence and development of the idea of area in Book 1, for in its enunciation the word ‘area’ is used for the very first time in the Elements. “In parallelogrammic areas,” Euclid posits, “the opposite sides and angles are equal to one another, and the

area of a parallelogram The area of the parallelogram is the absolute value of the determinant of the matrix formed by the vectors representing the parallelogram's sides. If the matrix entries are real numbers, the matrix A can be used to represent two linear maps: one that maps the standard basis vectors to the rows of A, and one that maps them to the columns of A