Class 9 Maths Chapter 6, Measuring Space: Perimeter and Area, is the mensuration chapter of Ganita Manjari and, at 37 pages, the longest in Part I. It opens with the staggered starting lines of a 4 × 100 m relay race and asks why runners in the outer lanes start ahead; working that out needs the perimeter of a circle, which leads to π, arc length, the areas of triangles and circles, Heron’s formula and Brahmagupta’s formula.
What Class 9 Maths Chapter 6 Covers
6.1 to 6.4 Perimeter, π and Arcs measure perimeters, estimate the C/D ratio of a circle at home, trace π from ancient approximations to Mādhava’s series π = 4(1 – 1/3 + 1/5 – 1/7 + …), explain that π is irrational, and derive the arc length l = 2πr × θ/360°.
6.5 Problems, Puzzles, and Paradoxes on Perimeter returns to the running track and solves the stagger with algebra.
6.6 to 6.9 Areas of Rectangles, Parallelograms and Triangles cover ½ × base × height, Heron’s formula A = √[s(s – a)(s – b)(s – c)], a note on special cases and generalisation in mathematics, and squaring a rectangle.
6.10 Area of a Circle derives A = πr² and the area of a sector, πr² × θ/360°.
Exercises in Chapter 6
- Exercise Sets 6.1 to 6.3: perimeter and arc problems, triangle and quadrilateral areas, and circle and sector areas.
- End-of-Chapter Exercises run over five pages, and the chapter summary lists the estimates of π by Archimedes, Zu Chongzhi (355/113), Āryabhaṭa (3.1416) and Mādhava.
Read Class 9 Maths Chapter 6 Online
More Chapters
- Previous: Chapter 5: I’m Up and Down, and Round and Round
- Next: Chapter 7: The Mathematics of Maybe: Introduction to Probability
- Hindi medium: Class 9 Maths Chapter 6 PDF in Hindi (समष्टि मापन — परिमाप और क्षेत्रफल)
- All Maths chapters and the other Class 9 books: Class 9 NCERT books 2026-27
- All Class 1 to 12 NCERT Textbooks: NCERT Books PDF (Class 1–12)
FAQ
Is Heron’s formula in the new Class 9 maths book?
Yes, in Chapter 6, section 6.8: the area of a triangle with sides a, b, c is √[s(s – a)(s – b)(s – c)], where s = (a + b + c)/2.
What is Brahmagupta’s formula?
The area of a cyclic quadrilateral with sides a, b, c, d is √[(s – a)(s – b)(s – c)(s – d)], with s half the perimeter. It appears in the Chapter 6 summary.