In the Sulba-Sutras, which are ancient Indian geometric texts that deal with the construction of altars Class 8

In the Sulba-Sutras, which are ancient Indian geometric texts that deal with the construction of altars Class 8

In the Sulba-Sutras, which are ancient Indian geometric texts that deal with the construction of altars, we can find many interesting problems on the topic of areas. When altars are built, they must have the exact prescribed shape and area. This gives rise to problems of the kind where one has to transform a given shape into another of the same area. The Sulb a-Sutras give solutions to many such problems.

Such problems are also posed and solved in Euclid’s Elements.

Here are two problems of this kind.

Question 1.

[Sulba-Sutras] Give a method to transform a rectangle into a triangle of equal area. Class 8

Solution:

(i) Let ABCD be a given rectangle.

(ii) Construct a line-segment EF equal to side AB of the rectangle.

(iii) At any point P of EF, draw a perpendi-cular XP.

(iv) Now, from XP, cut off a line-segment PQ = 2AD.

(v) Join EQ and FQ.

Then, QEF is the required triangle equal in area to the rectangle ABCD.