We will deduce formulas that allow us to calculate the notable segments of a triangle — heights, medians, internal angle bisectors, radii of the inscribed and circumscribed circles — knowing only the measurements of the sides. In all of them, the semiperimeter $p = \frac{a + b + c}{2}$ appears. The story The formula for the area on three sides is named after Heron of Alexandria (1st century), who demonstrated it in the Metric, a manual of practical measurements. The Persian mathematician al-Biruni, however, attributed it to Archimedes, two and a half centuries earlier. Heron’s demonstration is purely geometric, with the circumference inscribed; the one we will do here is algebraic, starting from the law of cosines.