NCERT Class 8 Mathematics Ganita Prakash Part-II: Chapter 2 — The Baudhayana-Pythagoras Theorem
This chapter from NCERT's Ganita Prakash Part-II for Class 8 Mathematics introduces the concept of 'Doubling a Square'. It explores a historical question posed by Baudhāyana in his Śulba-Sūtra (c. 800 BCE) about constructing a square with double the area of a given square. The text explains that simply doubling the side length quadruples the area. Baudhāyana's elegant solution involves constructing a square on the diagonal of the original square, which results in a square with double the area. The chapter uses visual aids and prompts critical thinking about why this construction works, relating it to congruent triangles formed by the diagonal and the sides. It encourages students to explore geometric constructions and understand area relationships.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Ganita Prakash Part-II |
| Chapter | Chapter 2 — The Baudhayana-Pythagoras Theorem |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 2 minutes |
| Word count | 381 |
Learning outcomes
- Understand the problem of doubling the area of a square.
- Learn Baudhāyana's solution using the diagonal of a square.
- Explain why a square constructed on the diagonal has double the area.
- Identify and reason about congruent triangles within the geometric construction.
- Appreciate the historical context of mathematical problems from the Śulba-Sūtra.
Vocabulary
| Word | Meaning |
|---|---|
| Baudhāyana | Ancient Indian mathematician and author of the Śulba-Sūtra. |
| Śulba-Sūtra | Ancient Indian texts containing rules for altar construction, dealing with geometry. |
| Diagonal | A line segment joining two non-adjacent vertices of a polygon. |
| Area | The extent or measurement of a surface or piece of land. |
| Square | A plane figure with four equal straight sides and four right angles. |
| Construct | To build or make something. |
| Congruent | Identical in form; coinciding exactly. |
| Vertices | A corner or point where two or more lines meet. |
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Practice questions
- If a square has a side length of 5 cm, what is its area? Answer: 25 sq cm.
- What happens to the area of a square if its side length is doubled? Answer: The area becomes four times the original area.
- According to Baudhāyana, how can a square with double the area be constructed? Answer: By constructing a square on the diagonal of the original square.
- Why does the new square constructed on the diagonal have double the area? Answer: Because the original square is made up of two small congruent triangles, and the new square is made up of four such congruent triangles.
Frequently asked questions
What is the main problem addressed in the chapter 'Doubling a Square'?
The chapter addresses how to construct a square that has exactly double the area of a given square.
Who proposed a solution to doubling a square's area historically?
Baudhāyana, in his Śulba-Sūtra (around 800 BCE), proposed a solution.
What is Baudhāyana's method for doubling the area of a square?
Baudhāyana's method is to construct a new square using the diagonal of the original square as its side.
Why does doubling the side length of a square not double its area?
Doubling the side length of a square results in an area that is four times the original area, not double.
How are congruent triangles related to doubling the area of a square?
The original square can be seen as composed of two congruent triangles, while the square on the diagonal is composed of four such congruent triangles, thus having double the area.
What is the significance of horizontal and vertical lines in this chapter?
These lines help visualize why the square constructed on the diagonal has double the area by showing how the original square is divided into congruent triangles.
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Topics covered
NCERT Class 8 Mathematics — Ganita Prakash Part-II — Chapter 2 — The Baudhayana-Pythagoras Theorem. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.