[Śulba-Sūtras] Give a method to convert an isosceles trapezium to a rectangle using dissection.
To convert an isosceles trapezium to a rectangle: (1) Take isosceles trapezium with parallel sides a and b (a > b) and height h. (2) Cut along the midline (line joining midpoints of non-parallel sides). (3) Alternatively, cut the two triangular portions from the ends and rearrange. (4) The resulting rectangle has length = (a + b)/2 and width = h. Area = h × (a + b)/2 = ½ × h × (a + b), which equals the trapezium's area.
Explanation
The chapter discusses dissection methods. An isosceles trapezium can be converted to a rectangle by cutting and rearranging the triangular portions at the ends.
Solution Steps
Step 1: Take isosceles trapezium with parallel sides a and b, height h.
Step 2: Cut the two triangular end portions.
Step 3: Rotate one triangle 180°.
Step 4: Join the triangles to form a rectangle.
Step 5: Rectangle dimensions: length = (a+b)/2, width = h.