Question 4 - Figure it out - Page 157-159 - Chapter 7 Class 8 - Area (Ganita Prakash II)

Transcript

Question 4 In the Śulba-Sūtras, 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 Śulba-Sūtras give solutions to many such problems. Such problems are also posed and solved in Euclid’s Elements. [Śulba-Sūtras] Give a method to transform a rectangle into a triangle of equal area.To turn it into a triangle with the exact same area, you can keep the base exactly the same length, but you must make the height of the triangle twice as tall as the rectangle. (Because the triangle formula halves the area, doubling the height perfectly balances it out!). Let’s look at it Step-by-Step Step 2: To change it to a triangle, first stretch a rope to DOUBLE the length of the base. Step 3: Build a new triangular shape connecting the original top corner to the new wide base. Area Base Height Area Base × Height Previous Result: The triangle is twice as wide, making up for its pointy top. The area remains EXACTLY the same!