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A Pinch of History

Historical Information on Mensuration: The Sulba Sutra, written around 800 BCE has a great amount
of knowledge on mensuration. To measure the length of an altar (Hawan Kunda) through sulba (rope)
they required a knowledge of different two-dimensional shapes like — triangles, rectangles, squares,
pentagons and to make the altar precise, it requires the knowledge of perimeter and area. Baudhayana
was the first to discuss the relationship between — hypotenuse, perpendicular and base and he was the
first, in fact hundreds of years before Pythagoras, who established the relation between the sides of
right angled triangle. Moreover, in order to perform the Yagna for going to heaven after death, Syancheti
, an altar in the form of a falcon was made, which contained five different shapes of bricks: right angled
triangles, pentagons, squares, rhombuses and trapeziums. A total of 1000 bricks in 5 layers with each layer
containing 200 bricks, were used. Performing such Yagnas required the knowledge of perimeter and area.
The book Bakshali Manuscript, written between 300-700 CE, also contains information on mensuration.
Aryabhata, in his book Goladhyaya provided a lot of information on mensuration. Even he derived many
formulas for spheres, triangles, etc. Bhaskaracharya in Lilavati, also dealt with area and perimeter.

Syenaciti–falcon shaped altar Five different size bricks used for making the altar

Mental Maths

1. What is the area of a rectangle whose length and breadth are 125 cm and 1 m respectively?
2. Find the cost of fencing a square park of side 250 m at the rate of `20 per metre.
3. A string is bent into a rectangular shape of length 20 cm and breadth 10 cm. If the string is re-bent into a
square shape, what would be the length of each side of the square?
4. How much distance is travelled by a person if he takes six rounds of a square park of side 80 m?
5. If the perimeter of a rectangular field is 320 m and its breadth is 60 m, then what will be its area?
6. In each figure, find the missing value of either the length of a side or the area of a region:
(a) ? cm (b)
? sq. cm
3 cm
5 cm
40 sq. cm 4 cm 42 sq. cm
16 cm

12 sq. cm 4 cm

66 sq. cm 6 cm

199 Perimeter and Area
199
and Ar
ea
P
erimeter