The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c8.t3.59

c8.t3.59

**3.12.** The rule of Baudhāyana suggests that the *Sautrāmaṇikī vedi* may be a square of 18 *padas* or an isosceles trapezium whose area is one-third of that of *mahāvedi*, having area of 972 sq. *padas*. Baudhāyana made no explicit mention of how to construct an isosceles trapezium similar to a given isosceles trapezium but with one-third of its area. Āpastamba (*Āśl.* 5.8) constructed it with 1/(√3) of the units used in *mahāvedi* or 8√3 and 10√3 as face and base and 12√3 as altitude. The *mahāvedi* is an isosceles trapezium having face 24, base 30 and altitude 36 units. Hence the *sautrāmaṇikī vedi* is an isosceles trapezium of face 24/(√3) or 8√3, base 30/(√3) or 10√3, and altitude 36/(√3) or 12√3. Hence the area of the figure in the above two cases comes out as,