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How is the area of a triangle calculated from its base and altitude?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia. — geometry This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

In Euclidean geometry, the area of a triangle is calculated by taking one-half of the product of its base ( $b$ ) and its altitude ( $h$ ). The formula is expressed as:

Area = $\frac{1}{2} b h$

In this context, the base is any side of the triangle, and the altitude is the perpendicular line segment extending from the opposite vertex to that base.1