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Baudhyana shulbasutra describes a method of converting a square to a circle as:

समचतुरस्त्रं दीर्घ चतुरस्त्रं चिकीर्षंस्तदक्ष्णया पच्छिद्य भागं द्वेधा विभज्य पार्श्वयोरुपदध्याद्यथायोगम्|| बौधायन शुल्बसुत्रम् १.५२||

“If you are desirous of converting a square into an oblong, divide it into two halves by the aksnaya(diagonal); divide again one half into two parts and adjust them in such a way that the required oblong is obtained.” (Baudhayana SulbaSutras 1.52)

Construct a square ABCD. Construct the diagonal across BD and mark its center as O. Construct the line OC. Place triangle BOC in the north and triangle DOC to the west of the square ABCD in such a way that the required oblong FDBE is obtained.

Square to Rectangle.png
Converting a square into a rectangle

We know angle E = angle F = 90 (Diagonals of a square divide the center into 4 parts of 90 each)

Hence FD || EB

Also FE = FA + AE = DO + OB = DB

And FD = EB.

Hence FDBE is a rectangle with an area  equal to that of the square ABCD

Computational tool for converting a square into a rectangle:

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