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The Jaina Antiquary
(Vol. XVII
4. TRAPEZIUM: The area of a trapezium is equal to half the sum of the lengths of its base and face multiplied by its height.
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Fig. 8.
The result follows from the construction shown in the'figure. The principle of deformation holds true in the case of a trapezium also, i.e. the area of the trapezium is unffected by a deformation brought about by moving one of the parallel sides in its own line.
5. SECTOR OF A CIRCLE: The area of a sector of a circle is equal to half the length of its arc multiplied by its radius.
Fig. 9.
Fig. 10.
Construction: Divide the sector
(Fig. 9) into a large number of smaller sectors (which may be equal), so that the arcs of these sub-sectors are so small that they differ little from straight lines. The sector is thus divided into a large number of triangles.
Now place these triangles with their bases abutting on one another on the line (see fig. 10) and move the vertices so that they all come to . The area of the sector is thus seen to be the is equal to the radius of the
same as the area of the triangle whose base length of the arc and whose height is equal to the
sector.
