The base of the pyramid is a formula_9 triangle formula_10, with edges of length formula_11, and formula_12 rising up to the apex formula_13 from points formula_14, formula_5, and formula_16 respectively. Base triangle formula_10 partitions into formula_18 and formula_19 triangles by dropping the perpendicular from point formula_16 to side formula_21. He proceeds to erect a triangle in the plane perpendicular to line formula_21 through the pyramid's apex, point formula_13, calculating all three sides of this triangle and noting that its height is the height of the pyramid. At the last step, he applies what amounts to this formula for the height formula_24 of a triangle in terms of its sides formula_25 (the height from side formula_26 to its opposite vertex):