Measuring Space: Perimeter and Area

Chapter at a glance

Perimeter and area of rectangles, parallelograms, triangles and circles: the C/D ratio π, arc length, sector area, Heron’s and Brahmagupta’s formulas, and puzzles and paradoxes.

What this chapter covers

• 6.1 Perimeter of a Shape
• 6.2 Perimeter of a Circle: the C/D Ratio
• 6.4 Length of an Arc of a Circle
• 6.5 Problems, Puzzles, and Paradoxes on Perimeter
• 6.6–6.8 Area of a Rectangle, Parallelogram and Triangle
• 6.9 Squaring a Rectangle
• 6.10 Area of a Circle

Key points

• π = circumference ÷ diameter for every circle (≈ 22/7 or 3.14); π is irrational. Āryabhaṭa gave π ≈ 3.1416; Mādhava gave π/4 = 1 − 1/3 + 1/5 − 1/7 + …
• C = 2πr; arc length = 2πr × θ/360°; circle area = πr²; sector area = πr² × θ/360°.
• Triangle area = ½ × base × height; Heron: √[s(s − a)(s − b)(s − c)] with s = (a + b + c)/2.
• Brahmagupta’s formula for a cyclic quadrilateral: √[(s − a)(s − b)(s − c)(s − d)], s = half the perimeter.

Read the NCERT chapter

Read this chapter in the official NCERT textbook Ganita Manjari (2026-27 edition) for free on ncert.nic.in.

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