NCERT Solutions for Class 9th Maths Chapter 6 Measuring Space: Perimeter and Area
Updated on 2026-09-08
About this chapter
For every circle the ratio of circumference to diameter is the same number, π . So C = 2πr = πd . π is irrational (Lambert, 1761), so no fraction equals it: π ≈ 22/7 but π ≠ 22/7 . Better approximations are 355/113 (Zu Chongzhi) and 3.1416 (Āryabhaṭa); Mādhava gave the first exact formula, π/4 = 1 − 1/3 + 1/5 − 1/7 + … A circle has rotational symmetry, so an arc turning through θ° at the centre is the fraction θ/360 of the whole circle. Hence arc length = 2πr × θ°/360° and area of a sector = πr² × θ°/360° . The half-turn and quarter-turn cases (πr and πr/2) are just θ = 180° and θ = 90°. Area of a rectangle = ab ; of a parallelogram = base × height (cut a triangle off one end and slide it to the other); of a triangle = ½ × base × height (two congruent copies make a parallelogram). The side
- Chapter opening: the 4 × 100 m relay track
- Perimeter of a Shape
- Perimeter of a Circle
- A Closer Look at a 400 m Athletics Track
- Problems, Puzzles, and Paradoxes on Perimeter
- Area of a Parallelogram
- Area of a Triangle
- Squaring a Rectangle
- Area of a Triangle and 6.9 Squaring a Rectangle
- Area of a Circle
Exercises
- Chapter opening: the 4 × 100 m relay track — In-text Questions Page 118
- Chapter opening: the 4 × 100 m relay track — Think and Reflect Page 118
- In-text Questions — Perimeter of a Shape Page 119
- Think and Reflect — Perimeter of a Shape Page 119
- In-text Questions — Perimeter of a Circle Page 120
- C/D's Adventurous Journey: From Ancient Approximations to the Exact Formula of Mādhava — In-text Questions Page 121
- A Closer Look at a 400 m Athletics Track — Think and Reflect Page 127
- Exercise Set 6.1 — Problems, Puzzles, and Paradoxes on Perimeter Page 129–130
- Think and Reflect — Area of a Parallelogram Page 131
- Think and Reflect — Area of a Parallelogram Page 131–132
- In-text Questions — Area of a Triangle Page 132
- In-text Questions — Area of a Triangle Page 133
- Think and Reflect — Area of a Triangle Page 133
- Think and Reflect — Area of a Triangle Page 134
- Think and Reflect — Squaring a Rectangle Page 142
- Exercise Set 6.2 — Area of a Triangle and 6.9 Squaring a Rectangle Page 142–143
- Think and Reflect — Area of a Circle Page 144
- In-text Questions — Area of a Circle Page 146
- Exercise Set 6.3 — Area of Sector of a Circle Page 148
- Whole chapter — End-of-Chapter Exercises Page 149–153